Yurko
Viacheslav
Anatolievich
- Post-graduate, Saratov University, Saratov, Russia, 1971-1974
- Assistant Professor, Saratov Polytechnical Institute, Saratov, Russia, 1974-1977.
- Associate Professor (Docent), Saratov University, Saratov, Russia, 1977-1991.
- Professor, Head of the Ghair of Mathematical Physics and Numerical Analysis, Saratov University, Saratov, Russia, 1991-present
V.A.Yurko was born on 28 August 1949 in Ozinki, Saratov district, Russia. In 1971 he received
his University Diploma in mathematics from Saratov State University (Department of Mathematics
and Mechanics). In 1971-1974 he was a post-graduate student of the same department. In 1975
V.A. Yurko received the Kandidat of Sciences degree (Ph.D.) from Saratov State University.
He was an assistant professor of mathematics in Saratov Polytechnical Institute (1974-1977)
and an associate professor (docent) of the Department of Mathematics and Mechanics in Saratov
State University (1977-1991). In 1992 he received the Doctor of Siences degree from Moscow State
University. Since 1991 he is a full professor of mathematics of the Department of Mathematics and
Mechanics in Saratov State University, and the Head of the Chair of Mathematical Physics and
Numerical Analysis.
Research interests of Prof. Yurko include spectral theory, theory of differential and integral
equations, mathematical physics, inverse problems, numerical analysis. The first thesis of
V.A. Yurko (for the Kandidat of Science degree (PhD), 1975) was devoted to uniqueness theorems
of recovering parameters of differential operators with desirable spectral properties. The method
developed in this work made it possible to describe the uniqueness classes for arbitrary order
differential operators on a finite interval.
The second thesis of V.A. Yurko (for the Doctor of Science degree, 1992) titled "Inverse Problems
for Differential Operators" was defended in Moscow State University. Inverse problems of spectral
analysis which consist in recovering operators from their spectral characteristics are of high
interest to many researchers due to the fundamental role that inverse problems play in various
areas of mathematics, natural sciences, and engineering. At the same time the nonlinearity of many
important classes of inverse problems makes them an extremely difficult area of research. That is
why by the end of the 1980s more or less complete results have been received only for Sturm-Liouville
and Dirac differential operators. In a major part of his works, Prof. Yurko has constructed the
inverse problem theory for arbitrary order differential operators and systems for regular and
singular cases. He has developed a new approach that allowed him to give the complete solution of
these classes of inverse spectral problems, obtain necessary and sufficient conditions for their
solvability, create numerical algorithms, and study stability properties of the solutions. Nowadays
his main method (called the method of spectral mappings) is the most universal tool for studying
invrse spectral problems for various classes of operators.
The important part of Prof. Yurko's works is devoted to the so-called incomplete inverse problems
that arise when only a part of spectral information is available. He has suggested a new method
(called the method of standard models) for constructing solutions of a wide class of incomplete
inverse problems, gave their classification, and described the degenerate cases. For differential
operators on the half-line the most difficult case for research is when the coefficients of the
differential equation grow at infinity. In part of his works devoted to these classes of operators,
V.A. Yurko introduced a new class of spectral characteristics in a special space of distributions
and gave the solution of the inverse problem for higher-order differential operators on the
half-line with locally integrable coefficients.
A number of important Yurko's works are devoted to boundary value problems on spatial networks
(geometrical graphs). Such problems often appear in natural sciences and engineering. In this part
of works Prof. Yurko created a general theory for constracting solutions of nonlinear inverse
problems for arbitrary spatial networks.
V.A. Yurko has also produced important results in the theory of boundary value problems for
differential equations with singularities and turning points, in the theory of non-local inverse
problems, in the theory of the so-called discontinuous boundary value problems and other major
areas of the theory of differential and integral equations and spectral theory.
An important part of Prof. Yurko s' works is devoted to the applications of spectral theory in
natural sciences and engineering. In particular, he has publications in elasticity theory, solid
mechanics, electronics, astrophysics, and theory of nonlinear waves.
In total V.A. Yurko has published more than 500 research articles and 10 monographs. He has
received over 60 research grants from various international and Russian funds.
MAIN MONOGRAPHS:
- Inverse Spectral Problems for Differential Operators and their Applications. Gordon and Breach, Amsterdam, 2000, 253pp.
- Inverse Sturm-Liouville Problems and their Applications, NOVA Science Publishers, New York, 2001, 305pp. (with Freiling G.).
- Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002, 303pp.
- Introduction to the theory of inverse spectral problems. Moscow, Fizmatlit, 2007, 384pp. (Russian).
- Lectures on Differential Equations of Mathematical Physics. NOVA Science Publishers, New York, 2008 (with Freiling G.).
MAIN RESEARCH PAPERS:
(1) Yurko V.A. An inverse problem for second order differential operators with
regular boundary conditions. Mat. Zametki, vol.18, no.4 (1975), 569-576;
English transl. in Math.Notes, vol.18, no.3-4 (1975), 928-932.
(2) Yurko V.A. Reconstruction of fourth-order differential operators.
Diff. Uravneniya, vol.19, no.11 (1983), 2016-2017.
(3) Yurko V.A. Boundary value problems with a parameter in the boundary conditions.
Izv. Akad. Nauk Armyan. SSR, Ser. Mat., vol.19, no.5 (1984), 398-409;
English transl. in Soviet J. Contemporary Math. Anal., vol.19, no.5 (1984), 62-73.
(4) Yurko V.A. An inverse problem for integral operators. Mat. Zametki, vol.37, no.5
(1985), 690-701; English transl. in Math. Notes, vol.37, no.5-6 (1985), 378-385.
(5) Yurko V.A. Uniqueness of the reconstruction of binomial differential operators
from two spectra. Mat. Zametki, vol.43, no.3 (1988), 356-364;
English transl. in Math. Notes, vol.43, no.3-4 (1988), 205-210.
(6) Yurko V.A. Reconstruction of higher-order differential operators.
Diff. Uravneniya, vol.25, no.9 (1989), 1540-1550;
English transl. in Diff. Equations, vol.25, no.9 (1989), 1082-1091.
(7) Yurko V.A. Inverse Problem for Differential Operators. Saratov, Saratov University
Press, 1989, 176pp. ISBN 5-292-00819-4
(8) Yurko V.A. Recovery of differential operators from the Weyl matrix.
Doklady Akad. Nauk SSSR, vol.313, no.6 (1990), 1368-1372;
English transl. in Soviet Math. Dokl., vol.42, no.1 (1991), 229-233.
(9) Yurko V.A. A problem in elasticity theory. Prikladnaya Matematika i Mekhanika,
vol.54, no.6 (1990), 998-1002; English transl. in J. Appl. Math. Mech., vol.54,
no.6 (1990), 820-824.
(10) Yurko V.A. Integration of the Boussinesq equation on the half-line.
Diff. Uravneniya, vol.27, no.9 (1991), 1647-1648.
(11) Yurko V.A. Solution of the Boussinesq equation on the half-line by
the inverse problem method. Inverse Problems, vol.7 (1991), 727-738.
(12) Yurko V.A. An inverse problem for differential operators on the half-line.
Izv. Vysshikh Uchebnykh Zavedenii, Ser. Mat., no.12 (1991), 67-76;
English transl. in Soviet Math. (Iz.VVZ), vol.35, no.12 (1991), 67-74.
(13) Yurko V.A. Recovery of nonselfadjoint differential operators on the half-line
from the Weyl matrix. Mat. Sbornik, vol.182, no.3 (1991), 431-456;
English transl. in Math. USSR Sbornik, vol.72, no.2 (1992), 413-438.
(14) Yurko V.A. On determination of differential operators on the half-line.
Doklady Akad. Nauk Ukrainy, no.9 (1991), 34-37.
(15) Yurko V.A. An inverse problem for integro-differential operators. Mat. zametki,
vol.50, no.5 (1991), 134-146; English transl. in Math. Notes, 50, no.5-6 (1991),
1188-1197.
(16) Yurko V.A. Inverse problem for differential equations. Uspekhi Mat. Nauk,
vol.46, no.6 (1991), 148-149.
(17) Yurko V.A. Inverse problem for differential equations with a singularity.
Diff. Uravneniya, vol.28, no.8 (1992), 1355-1362;
English transl. in Diff. Equations, vol.28 (1992), 1100-1107.
(18) Yurko V.A. Inverse problem for differential equations. Dokt. Thesis, Moscow,
Moscow State University, 1992, 328pp.
(19) Yurko V.A. On higher-order differential operators with a singular point.
Inverse Problems, vol.9 (1993), 495-502.
(20) Yurko V.A. Inverse problem for selfadjoint differential operators on the half-line.
Doklady RAN, vol.333, no.4 (1993), 449-451; English transl. in Russian Acad.
Sci Dokl. Math., vol.48, no.3 (1994), 583-587.
(21) Yurko V.A. Inverse problem for higher-order differential equations with a singular
point. Izv. Vysshikh Uchebnykh Zavedenii, Ser. Mat., no.7 (1993), 59-68;
English transl. in J. Russ. Math., vol.37, no.7 (1993), 58-66.
(22) Yurko V.A. Inverse problem for a nonlinear differential equation on the half-line.
Uspekhi Mat. Nauk, vol.48, no.4 (1993), 210-211.
(23) Yurko V.A. On differential operators with nonseparated boundary conditions.
Funkt. Analiz i Prilozh., vol.28, no.4 (1994), 90-92; English transl. in Funct.
Anal. and Appl., vol.28, no.4 (1994), 295-297.
(24) Yurko V.A. On higher order differential operators with a singularity.
Uspekhi Mat. Nauk, vol.49, no.4 (1994), 90-91.
(25) Yurko V.A. On inverse problems for nonlinear differential equations.
Diff. Uravneniya, vol.31, no.10 (1995), 1768-1769;
English transl.in Diff. Equations, vol.31, no.10 (1995), 1741-1743.
(26) Yurko V.A. On higher-order difference operators. J. Difference Equations and Appl.,
vol.1 (1995), 347-352.
(27) Yurko V.A. On higher-order differential operators with a singularity.
Mat. Sbornik, vol.186, no.6 (1995), 133-160; English transl.
in Sbornik; Mathematics vol.186, no.6 (1995), 901-928.
(28) Yurko V.A. On determination of selfadjoint differential operators on the half-line.
Mat. Zametki, vol.57, no.3 (1995), 451-462;
English transl. in Math. Notes, vol.57, no.3-4 (1995), 310-318.
(29) Yurko V.A. On integration of nonlinear dynamical systems by the inverse problem
method. Mat. Zametki, vol.57, no.6 (1995), 945-949; English transl. in Math. Notes,
vol.57, no.6 (1995), 672-675.
(30) Yurko V.A. On higher order differential operators with a singularity.
Uspekhi Mat. Nauk, vol.50, no.4 (1995), 124-125.
(31) Yurko V.A. Boundary value problems for a differential equation with a singularity.
Doklady Akad. Nauk, vol.349, no.4 (1996), 460-462; English transl. in Doklady
Mathematics, vol.54, no.1 (1996), 571-573.
(32) Yurko V.A. On discrete operators of higher order. Uspekhi Mat. Nauk, vol.51, no.3
(1996), 217-218; English transl.in Russian Math. Surveys, vol.51, no.3 (1996),
578-580.
(33) Yurko V.A. On higher-order difference operators. Algebraic
and Geometric Methods in Mathematical Physics, c.463-469; Math. Phys. Stud.
19, Kluwer Academic Publishers, Dordrecht, 1996.
(34) Yurko V.A. An inverse problems for operators of a triangular structure.
Results in Mathematics, vol.30, no.3-4 (1996), 346-373.
(35) Yurko V.A. Quaternion construction of the optimal control and paths of motion of
a spacecraft in the Newton gravitational field. Izvestija RAN, Mechanika tverdogo
tela, no.6 (1996), 3-13 (with Chelnokov Y.N.).
(36) Yurko V.A. On higher order differential operators with a singularity.
Uspekhi Mat. Nauk, vol.51, no.5 (1996), 155-156.
(37) Yurko V.A. An inverse problem for systems of differential equations with nonlinear
dependence on the spectral parameter. Diff. Uravneniya, vol.33, no.3 (1997),
390-395; English transl. in Diff. Equations, vol.33, no.3 (1997), 388-394.
(38) Yurko V.A. Inverse problems for differential equations with turning points.
Inverse Problems, vol.13 (1997), 1247-1263 (with Freiling G.).
(39) Yurko V.A. Integral transforms connected with differential operators having
singularities inside the interval. Integral Transforms and Special Functions,
vol.5, no.3-4 (1997), 309-322.
(40) Yurko V.A. Sturm-Liouville differential operators with singularities.
Spectral and Scattering Theory, c.199-205; Plenum, New York, 1998.
(41) Yurko V.A. Expansion theorems for boundary value problems with a singularity.
Analysis, vol.18 (1998), 25-39 (with Freiling G.).
(42) Yurko V.A. On constructing differential equations with singularities from
incomplete spectral information. Inverse Problems, vol.14, no.5 (1998), 1131-1150
(with Freiling G.)
(43) Yurko V.A. Integrable dynamical systems connected with higher-order difference
operators. Izv. Vysshikh Uchebnykh Zavedenii, Ser. Mat., no.10 (1998), 71-81;
English transl. in Russian Math. (Izv. VUZ), vol.42 (1998), no.10, 69-79.
(44) Yurko V.A. On recovering Sturm-Liouville differential operators with singularities
inside the interval. Mat. Zametki, vol.64, no.1 (1998), 143-156; English transl.
in Math. Notes, vol.64, no.1 (1998), 121-132.
(45) Yurko V.A. Inverse spectral problems for differential operators and their applications.
Itogi Nauki i tekhniki. Sovrem. Mat., vol.54, VINITI, Moscow, 1998, 117pp.
(46) Yurko V.A. Inverse spectral problems for differential equations on the half-line
with turning points. Journal of Differential Equations, vol.154 (1999), 419-453
(with Freiling G.).
(47) Yurko V.A. Reconstructing parameters of a medium from incomplete spectral
information. Results in Mathematics, vol.35 (1999), 228-249 (with Freiling G.).
(48) Yurko V.A. On reconstruction of second-order quadratic pencils on
the half-line. Journal of Science and Engineering, vol.11, no.3 (1999), 351-356.
(49) Yurko V.A. Inverse Spectral Problems for Differential Operators and their Applications.
Gordon and Breach Science Publishers, Amsterdam, 2000, 253pp. ISBN: 90-5699-189-2.
(50) Yurko V.A. On boundary value problems with jump conditions inside the interval.
Differ. Uravn., vol.36 (2000), no.8, 1139-1140; English transl. in Diff. Equations,
(2000), no.8, 1266-1269.
(51) Yurko V.A. Integral transforms connected with discontinuous boundary value
problems. Integral Transforms and Special Functions, vol.10, no.2 (2000), 141-164.
(52) Yurko V.A. Inverse spectral problems for differential operators and
their applications. Journal of Mathematical Sciences (New York), vol.98, no.3
(2000), 319-426.
(53) Yurko V.A. Inverse problems for differential equations with singularities lying inside
the interval. Journal of Inverse and Ill-Posed Problems, vol.8, no.1 (2000), 89-103.
(54) Yurko V.A. The inverse spectral problem for differential operators with nonseparated
boundary conditions. Journal of Mathematical Analysis and Applications, vol.250
(2000), 266-289.
(55) Yurko V.A. An inverse problem for pencils of differential operators. Mat. Sbornik,
vol.191 (2000), no.10, 137-160; English transl. in Sbornik: Mathematics, vol.191
(2000), no.10, 1561-1586.
(56) Yurko V.A. On recovery of pencils of differential operators on the half-line.
Matemat. Zametki, vol.67, no.2 (2000), 316-319; English transl.in Math. Notes, vol.67
(2000), no.2, 261-265.
(57) Yurko V.A. An inverse problem for differential equations of the Orr-Sommerfeld type.
Mathematishe Nachrichten, vol.211 (2000), 177-183.
(58) Yurko V.A. Inverse Sturm-Liouville Problems and their Applications.
NOVA Science Publishers, New York, 2001, 305p. (with Freiling G.). ISBN 1-56072-909-0
(59) Yurko V.A. Inverse Spectral Problems and their Applications. Saratov, PI Press, 2001,
499pp. ISBN 5-87077-059-9.
(60) Yurko V.A. Recovery of differential equations with nonlinear dependence on the
spectral parameter. Applicable Analysis, vol.78, no.1-2 (2001), 63-77.
(61) Yurko V.A. Yurko V.A. On differential operators with a singularity and discontinuity
conditions inside the interval. Ukrain. Mat. Zh., vol.53, no.11 (2001), 1443-1457;
English transl. in Ukrainian Math. J., vol.53, no.11 (2001), 1751-1770 (with Amirov R.).
(62) Yurko V.A. Method of Spectral Mappings in the Inverse Problem Theory.
Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002, 303pp. ISBN 90-6764-355-6
(63) Yurko V.A. Spectral analysis for an indefinite singular Sturm-Liouville problem.
Applicable Analysis, vol.81, no.6 (2002), 1283-1305 (with Freiling G. and Rykhlov V.).
(64) Yurko V.A. On recovering singular non-selfadjoint differential operators with a
singularity inside the interval. Differen. Uravn., vol.38, no.5 (2002), 645-659;
English transl. in Differen. Equations, vol.38, no.5 (2002), 678-694.
(65) Yurko V.A. Inverse spectral problems for singular non-selfadjoint differential operators
with discontinuties in an interior point. Inverse Problems, vol.18 (2002), 757-773
(with Freiling G.).
(66) Yurko V.A. Integral transforms connected with higher-order differential operators with
a singularity. Integral Transforms and Special Functions, vol.13, no.6 (2002), 497-511.
(67) Yurko V.A. Inverse spectral problems for higher-order differential operators with a
singularity. Journal of Inverse and Ill-Posed Problems, vol.10, no.4 (2002), 413-425.
(68) Yurko V.A. On higher-order differential operators with a singularity inside the
interval. Matemat. Zametki, vol.71, no.1 (2002) 152-156; English transl. in Math.
Notes, vol.71 (2002), no.1-2, 141-145.
(69) Yurko V. On the determination of differential equations with singularities and
turning points. Results in Mathematics, vol.41 (2002), 275-290 (with Freiling G.).
(70) Yurko V.A. Higher-order differential equations having a singularity in an
interior point. Results in Mathematics, vol.42 (2002), 177-191.
(71) Yurko V.A. Half-range expansions for an astrophysical problem. Letters in
Mathematical Physics, vol.64 (2003), 65-73 (with Freiling G. and Vietri M.).
(72) Yurko V.A. Spectral analysis for differential operators with singularities.
Abstract and Applied Analysis, vol. 2004 (9), no.2 (2004), 165-182.
(73) Yurko V.A. Necessary and sufficient conditions for the solvability of the inverse
problem for systems of differential equations on the half-line. Doklady Akad. Nauk,
vol.396, no.6 (2004), 755-758; English transl. in Doklady Mathematics, vol.69, no.3
(2004), 465-468.
(74) Yurko V.A. An inverse spectral problem for singular non-selfadjoint differential
systems. Mat. Sbornik, vol.195, no. 12 (2004), 123-156; English transl. in Sbornik:
Mathematics, vol.195, no.12 (2004), 1823-1854.
(75) Yurko V.A. On recovering non-selfadjoint differential systems on the half-line from
the Weyl matrix. Matemat. Zametki, vol.76, no.2 (2004), 316-320; English transl. in
Math. Notes, vol.76, no.2 (2004), 296-302.
(76) Yurko V.A. The inverse problem method on the half-line and a nested system of Riccati
equations. Results in Mathematics, vol.45, no.3-4 (2004), 246-253 (with Freiling G.).
(77) Yurko V.A. Equations in Mathematical Physics. Saratov Uni. Press, Saratov, 2004,
120pp. ISBN 5-292-03022-8.
(78) Yurko V.A. Nested Riccati equations connected with a completely
integrable systems and related topics. Math. Theory of Networks and
Systems, Leuven University Press, Leuven, 2004, pp.1-8 (with Freiling G.).
(79) Yurko V.A. An inverse problem for differential systems on a finite interval in the
case of multiple roots of the characteristic polynomial. Diff. Uravn., vol.41, no.6
(2005), 781-786; English transl. in Diff. Equations, vol. 41, no.6 (2005), 818-823.
(80) Yurko V.A. The Weyl-type matrix and the method of spectral mappings in the inverse
problem theory. Far East Journal of Applied Mathematics, vol.19, no.2 (2005),
125-146 (with Freiling G.).
(81) Yurko V.A. Boundary value problems with regular singularities and singular boundary
conditions. International Journal of Mathematics and Mathematical Sciences, vol.2005,
no.9 (2005), 1481-1495 (with Freiling G.).
(82) Yurko V.A. Inverse spectral problems for Sturm-Liouville operators on graphs.
Inverse Problems, vol. 21, no.3 (2005), 1075-1086.
(83) Yurko V.A. An inverse problem for differential systems with multiplied roots of the
characteristic polynomial. Journal of Inverse and Ill-Posed Problems, vol.13, no.5
(2005), 503-512.
(84) Yurko V.A. Inverse problems for differential operators with singular boundary conditions.
Mathematishe Nachrichten, vol.278, no.12-13 (2005), 1561-1578 (with Freiling G.).
(85) Yurko V.A. Inverse spectral problems for differential systems on a finite
interval. Results in Mathematics, vol.48, no.3/4 (2005), 371-386.
(86) Yurko V.A. An inverse problem of spectral analysis for differential systems
on the half-line. Mathematica Balkanica, vol.19, no. 1-2 (2005), 233-240.
(87) Yurko V.A. The inverse problem for pencils of differential operators on the half-line
with turning points. Fund. Prikl. Mat., vol.12, no.5 (2006), 237-246.
(88) Yurko V.A. An inverse problems for the matrix Sturm-Liouville equation
on a finite interval. Inverse Problems, vol.22 (2006), 1139-1149.
(89) Yurko V.A. Inverse spectral problems for differential pencils on the half-line with
turning points. Journal of Mathematical Analysis and Applications, vol.320 (2006),
439-463.
(90) Yurko V.A. On recovering Sturm-Liouville operators on graphs. Matem. Zametki, vol.79,
no.4 (2006), 619-630; English transl. in Math. Notes, vol.79, no.4 (2006), 572-582.
(91) Yurko V.A. Inverse problems for matrix Sturm-Liouville operators.
Russian Journal of Mathematical Physics, vol.13, no.1 (2006), 111-118.
(92) Yurko V.A. On recovering differential systems on a finite interval from spectra.
Trudy MIRAN Steklov, vol.255 (2006), 273-287; English transl. in Proceedings of the
Steklov Institute of Mathematics, vol.255 (2006),260-274.
(93) Yurko V.A., Introduction to the theory of inverse spectral problems. Moscow, Fizmatlit,
2007, 384pp. ISBN 978-5-9221-0734-8.
(94) Yurko V.A. A numerical algorithm for solving inverse problems for singular
Sturm-Liouville operators. Advances in Dynamical Systems and Applications,
vol.2, no.1 (2007), 95-105 (with Freiling G. and Mazur T.).
(95) Yurko V.A. Inverse problems for differential operators on graphs with general matching
conditions. Applicable Analysis, vol.86, no.6 (2007), 653-667 (with Freiling G.).
(96) Yurko V.A. An inverse problem for higher-order differential operators on
star-type graphs. Inverse Problems, vol.23 (2007), 893-903.
(97) Yurko V.A. An inverse problems for the non-selfadjoint matrix Sturm-Liouville
equation on the half-line. Journal of Inverse and Ill-Posed Problems, vol.15,
no.8 (2007), 785-798 (with Freiling G.).
(98) Yurko V.A. Inverse spectral problems for Sturm-Liouville operators on noncompact
trees. Results in Mathematics, vol.50 (2007), 195-212 (with Freiling G.).
(99) Yurko V.A. Lectures on Differential Equations of Mathematical
Physics. NOVA Science Publishers, New York, 2008, 250pp. (with
Freiling G.). ISBN 978-1-60456-928-5.
(100) Yurko V.A. Recovering higher-order differential operators on star-type graphs
from spectra. Cubo Mathematical Journal, vol.10, no.1 (2008), 93-102.
(101) Yurko V.A. Reconstruction of higher-order differential operators on compact graphs.
Doklady Akad. Nauk, vol.419, no.5 (2008), 604-608; English transl. in Doklady
Mathematics, vol.77, no.2 (2008), 293-297.
(102) Yurko V.A. An inverse spectral problem for pencils of differential operators on
noncompact networks. Differ. Uravnen., vol.44, no.12 (2008), 1658-1666; English
transl. in Diff. Equations, vol.44, no.12 (2008), 1721-1729.
(103) Yurko V. Numerical solution of the inverse synthesis problem for stratified media
from incomplete spectral information. Far East Journal of Mathematical Sciences,
vol.31, no.3 (2008), 361-376 (with Freiling G. and Galkin G.).
(104) Yurko V.A. Recovering differential pencils on compact graphs.
Journal of Differential Equations, vol.244 (2008), 431-443.
(105) Yurko V.A. Inverse nodal and inverse spectral problems for differential operators
on graphs. Journal of Inverse and Ill-Posed Problems, vol.16, no.7 (2008), 715-722.
(106) Yurko V.A. Inverse spectral and nodal problems for discontinuous boundary value
problems. Journal of Mathematical Analysis and Applications, vol.347, no.1 (2008),
266-272 (with Chung-Tsun Shieh).
(107) Yurko V.A. The inverse problem for pencils of differential operators on the half-line
with turning points. Journal of Math. Sciences, vol.150, no.6 (2008), 2620-2627.
(108) Yurko V.A. Inverse problems for differential of any order on trees. Matemat. Zametki,
vol.83,no.1 (2008), 139-152; English transl. in Math. Notes, vol.83, no.1 (2008),
125-137.
(109) Yurko V.A. Inverse problems for Sturm-Liouville operators on graphs with a cycle.
Operators and Matrices, vol.2, no.4 (2008), 543-553.
(110) Yurko V.A. An inverse spectral problem for Sturm-Liouville operators with singular
potentials on star-type graphs. Analysis on Graphs and its Applications, vol.77,
pp.397-408, Amer. Math. Soc., Providence, 2008 (with Freiling G. and Ignatiev M.).
(111) Yurko V.A. Numerical methods for solving inverse Sturm-Liouville problems.
Results in Mathematics, vol.52, no.1-2 (2008), 63-74 (with Ignatiev M.Yu.).
(112) Yurko V. Uniqueness of recovering differential operators on hedgehog-type graphs.
Advances in Dynamical Systems and Appl., vol.4, no.2 (2009), 231-241.
(113) Yurko V.A. On an inverse spectral problem for differential operators on a
hedgehog-type graph. Doklady Akad. Nauk, vol.425, no.4 (2009), 466-470;
English transl: Doklady Mathematics, vol.79, no.2 (2009), 250-254.
(114) Yurko V.A. Inverse problems for Sturm-Liouville operators on bush-type graphs.
Inverse Problems, vol.25, no.10 (2009), paper 105008, 14pp.
(115) Yurko V.A. Inverse spectral problems for Sturm-Liouville differential operators on
a finite interval. Journal of Inverse and Ill-Posed Problems, vol.17, no.7 (2009),
639-694.
(116) Yurko V.A. Recovering Sturm-Liouville operators from spectra on a graph with a cycle.
Matem. Sbornik, vol.200, no.9 (2009), 147-160; English transl. in Sbornik:
Mathematics, vol. 200, no.9 (2009), 1403-1415.
(117) Yurko V.A. Uniqueness of recovering Sturm-Liouville operators on A-graphs
from spectra. Results in Mathematics, vol.55, no.1-2 (2009), 199-207.
(118) Yurko V.A. Inverse nodal problems for Sturm-Liouville differential operators on a
star-type graph. Sibir. Mat. Zh., vol.50, no.2 (2009), 467-473;
English transl: Siberian Math. Journal, vol.50, no.2 (2009), 373-378.
(119) Yurko V.A. Inverse spectral problems for differential operators on a graph
with a rooted cycle. Tamkang Journal of Mathematics, vol.40, no.3 (2009), 271-286.
(120) Yurko V.A. An inverse problem for Sturm-Liouville operators on A-graphs.
Applied Mathematical Letters, vol.23, no.8 (2010), 875-879.
(121) Yurko V.A. An inverse problem for Sturm-Liouville operators on arbitrary compact
spatial networks. Doklady Akad. Nauk, vol.432, no.3 (2010), 318-321;
English transl: Doklady Mathematics, vol.81, no.3 (2010), 410-413.
(122) Yurko V.A. Inverse problems for Sturm-Liouville equations with boundary
conditions polynomially dependent on the spectral parameter. Inverse Problems,
vol.26, no.5 (2010), paper 055003, 17pp. (with Freiling G.).
(123) Yurko V.A. Inverse spectral problems for differential operators on arbitrary compact
graphs. Journal of Inverse and Ill-Posed Problems, vol.18, no.3 (2010), 245-261.
(124) Yurko V.A. A remark on inverse problems for Sturm-Liouville operators on graphs.
Results in Mathematics, vol.58 (2010), 399-401.
(125) Yurko V.A. Inverse nodal problems for differential operators on graphs with a cycle.
Tamkang Journal of Mathematics, vol.41, no.1 (2010), 15-24 (with Freiling G.).
(126) Yurko V.A. Equations in Mathematical Physics. Nauka, Saratov, 2010, 157pp.
ISBN 978-5-9999-0469-0.
(127) Yurko V.A. Recovering singular Sturm-Liouville differential pencils from the
spectral data. Analysis and Mathematical Physics, vol.1, no.1 (2011), 47-67.
(128) Yurko V.A. On the stability of constructing a potential in the central symmetry
case. Applicable Analysis, vol.90, no.12 (2011), 1819-1828 (with G. Freiling).
(129) Yurko V.A. Reconstruction of Sturm-Liouville differential operators on A-graphs.
Differen. Uravn., vol.47, no.1 (2011), 50-59; English transl. in Differen. Equations,
vol.47, no.1 (2011), 50-59.
(130) Yurko V.A. Inverse problems for Bessel-type differential equations on noncompact
graphs using spectral data. Inverse Problems, vol.27 (2011), paper 045002, 17pp.
(131) Yurko V.A. Inverse problem for Sturm-Liouville operators on hedgehog-type graphs.
Matemat. Zametki, vol.89, no.3 (2011), 459-471; English transl. in Math. Notes,
vol.89, no.3 (2011), 438-449.
(132) Yurko V.A. Recovering singular differential operators on noncompact star-type graphs
from Weyl functions. Tamkang Journal of Mathematics, vol.42, no. 2 (2011), 223-236.
(133) Yurko V.A. Necessary and sufficient conditions for the solvability of the
inverse problem for non-self-adjoint pencils of Sturm-Liouville operators on
the half-line. Tamkang Journal of Mathematics, vol.42, no.3 (2011), 247-258.
(134) Yurko V.A. Inverse problems for non-selfadjoint quasi-periodic differential
pencils. Analysis and Mathematical Physics, vol.2, no.3 (2012), 215-230.
(135) Yurko V.A. Determination of singular differential pencils from the Weyl function.
Advances in Dynamical Systems and Applications, vol.7, no.2 (2012), 171-193
(with G. Freiling).
(136) Yurko V.A. Inverse problems for differential operators with a constant delay.
Applied Mathematics Letters, vol.25, no.11 (2012), 1999-2004 (with G. Freiling).
(137) Yurko V.A. Inverse problems for second-order differential pencils with Dirichlet
boundary conditions. Journal of Inverse and Ill-Posed Problems, vol.20, no.5-6
(2012), 855-881 (with Buterin S.A.).
(138) Yurko V.A. Inverse spectral problems for arbitrary order differential operators on
noncompact trees. Journal of Inverse and Ill-Posed Problems, vol.20, no.1 (2012),
111-132.
(139) Yurko V.A. Recovering arbitrary order differential operators on noncompact
star-type graphs. Methods Funct. Analysis and Topology, vol.18, no.1 (2012), 90-100.
(140) Yurko V.A. An inverse spectral problem for non-selfadjoint Sturm-Liouville
operators with nonseparated boundary conditions. Tamkang Journal of Mathematics,
vol.43, no.2 (2012), 289-299.
(141) Yurko V.A. On Ambarzumyan-type theorems. Applied Mathematical Letters, vol.26,
no.4 (2013), 506-509.
(142) Yurko V.A. Inverse spectral problems for non-selfadjoint second-order
differential operators with Dirichlet boundary conditions. Boundary Value
Problems, 2013:180 (2013), 1-24 (with S.A. Buterin and C.-T. Shieh).
(143) Yurko V.A. Recovering variable order differential operators on star-type graphs from
spectra. Differ. Uravneniya, vol.49, no.12 (2013), 1537-1548; English transl. in
Differ. Equations, vol.49, no.12 (2013), 1490-1501.
(144) Yurko V.A. Inverse problems for differential operators of variable orders on
star-type graphs: general case. Analysis and Mathematical Physics, vol.4, no.3
(2014), 247-262.
(145) Yurko V.A. Inverse problems on star-type graphs: differential operators of
different orders on different edges. Central European Journal of Mathematics,
vol.12, no.3 (2014), 483-499.
(146) Yurko V.A. An inverse problem for differential operators on hedgehog-type
graphs with general matching conditions. Communications in Mathematical
Analysis, vol.17, no.2 (2014), 98-107 (with Choque Rivero A. and Karlovich Yu.).
(147) Yurko V.A. Recovering Sturm-Liouville operators on hedgehog-type graphs with
general matching conditions. Eurasian Mathematical Journal, vol.5, no.4 (2014),
56-69 (with Freiling G.).
(148) Yurko V.A. An inverse spectral problems for integro-differential operators.
Far East Journal of Mathematical Sciences, vol.92, no.2 (2014), 247-261.
(149) Yurko V.A. An inverse problem for differential pencils on graphs with a cycle.
Journal of Inverse and Ill-Posed Problems, vol.22, no.5 (2014), 625-641.
(150) Yurko V.A. Inverse problems for differential systems on graphs with regular
singularities. Mathematical Notes, vol.96, no.4 (2014), 617-621.
(151) Yurko V.A. Recovering differential pencils on graphs with a cycle from spectra.
Tamkang Journal of Mathematics, vol.45, no.2 (2014), 195-206.
(152) Yurko V.A. Inverse problem for differential operators on spatial networks with
different orders on different edges. Trudy Moscow Math. Soc., vol.75, no.2 (2014),
125-138.
(153) Yurko V.A. Recovering non-selfadjoint differential pencils with nonseparated
boundary conditions. Applicable Analysis, vol.94, no.8 (2015), 1649-1661
(with G. Freiling).
(154) Yurko V.A. On an open question in the inverse transmission eigenvalue problem.
Inverse Problems, vol.31 no.4 (2015), paper 045003 (with S. Buterin and C-F. Yang).
(155) Yurko V.A. Inverse problems for variable order differential operators with
regular singularities on graphs. Journal of Inverse and Ill-Posed Problems,
vol.23, no.6 (2015), 647-656.
(156) Yurko V.A. On an inverse problem for quasi-periodic differential pencils with jump
conditions inside the interval. Matemat. Zametki, vol.98, no.3 (2015), 476-480;
English transl. in Mathematical Notes, vol.98, no.3 (2015), 529-533.
(157) Yurko V.A. Inverse problems for higher order differential systems with regular
singularities on star-type graphs. Tamkang Journal of Mathematics, vol.46,
no.3 (2015), 257-268.
(158) Yurko V.A. Recovering differential operators with nonlocal boundary conditions.
Analysis and Mathematical Physics, vol.6, no.4(2016), 315-326 (with Yang C-F.).
(159) Yurko V.A. Inverse problem for Dirac system with singularities in interior points.
Analysis and Mathematical Physics, vol.6, no.1 (2016), 1-29 (with Gorbunov O.).
(160) Yurko V.A. Inverse spectral problems for differential operators
on spatial networks.
Uspekhi Mat. Nauk, vol.71, no.3 (2016), 149-196; English transl. in Russian
Mathematical Surveys, vol.71, no.3 (2016), 539-584.
REVIEW ARTICLE
(161) Yurko V.A. Dirac system with a singularity in an interior point. Applicable
Analysis, vol.95, no.11 (2016), 2397-2414 (with Gorbunov o.B. and Shieh C-T.).
(162) Yurko V.A. Inverse problem for quasi-periodic differential pencils with jump
conditions inside the interval. Complex Analysis and Operator Theory, vol.10,
no.6 (2016), 1203-1212.
(163) Yurko V.A. Inverse problem for differential pencils on a hedgehog-type graph.
Differen. Uravn., vol.52, no.3 (2016), 342-351; English transl. in Differential
Equations, vol.52, no.3 (2016), 335-345.
(164) Yurko V.A. Inverse spectral problems for differential pencils on a graph with
a rooted cycle. Inverse Problems in Science and Engineering, vol.24, no.9 (2016), 1647-1660.
(165) Yurko V.A. On the inverse nodal problems for discontinuous Sturm-Liouville
operators. Journal of Differential Equations, vol.260, no.5 (2016), 4086-4109
(with Yu-Ping Wang).
(166) Yurko V.A. Recovering Dirac operator with nonlocal boundary conditions.
Journal of Mathematical Analysis and Applications, vol.440, no.1 (2016), 155-166
(with Chuan-Fu Yang).
(167) Yurko V.A. Inverse problems for the first-order integro-differential operators.
Matemat. Zametki, vol.100, no.6 (2016), 939-946; English transl. in Mathematical
Notes, vol.100, no.6 (2016), 876-882.
(168) Yurko V.A. Theory of Entire Functions and its Applications.
Lambert Academic Publishing, Berlin, 2016, 81pp. ISBN: 978-3-659-88236-4.
(169) Yurko V.A. Inverse problems for second order integro-differential operators.
Apllied Mathematics Letters, vol.74 (2017), 1-6.
(170) Yurko V.A. Inverse spectral problems for first order integro-differential operators.
Boundary value problems (2017), 2017:98, 7pp. DOI: 10.1186/s13661-017-0831-8 (2017).
(171) Yurko V.A. Inverse problems for differential pencils on A-graphs. Journal of
Inverse and Ill-Posed Problems, vol.25, no.6 (2017), 819-828.
(172) Yurko V.A. Inverse spectral problems for differential pencils with boundary
conditions dependent on the spectral parameter. Mathematical Methods in the
Applied Sciences, vol.40, no.8 (2017), 3190-3196 (with Wang Y-P.).
(173) Yurko V.A. Sturm-Liouville differential operators with deviating argument. Tamkang
Journal of Mathematics, vol.48, no.1 (2017), 61-71 (with Buterin S., Pikula M.).
(174) Yurko V.A. Inverse problems for differential operators with nonseparated
boundary conditions in the central symmetric case. Tamkang Journal of Mathematics,
vol.48, no.4 (2017), 377-387.
(175) Yurko V.A. Inverse problems for differential pencils on bush-type graphs.
Results in Mathematics, vol.71, no.3 (2017), 1047-1062.
(176) Yurko V.A. Spectral analysis of higher-order differential operators with
discontinuity conditions at an interior point. Modern Mathematics. Fundamental
Areas, vol.63, no.2 (2017), 362-372.
(177) Yurko V.A. On the missing eigenvalue problem for Dirac operators.
Applied Mathematics Letters, vol.80 (2018), 41-47 (with Wang Y.Р.).
(178) Yurko V. An inverse problem for Sturm-Liouville differential
operators with deviating argument. Applied Mathematics Letters, vol.83 (2018), 140-144
(with Bondarenko N.).
(179) Yurko V.A. Inverse spectral problems for Sturm-Liouville
operators with complex weights. Inverse Problems in Science and
Engineering, 26, no.10 (2018), 1396-1403.
(180) Yurko V.A. On the determination of differential pencils with
nonlocal boundary conditions. Journal of Inverse and Ill-Posed Problems,
vol.26, no.5 (2018), 577-588 (with Yang C-F.).
(181) Yurko V.A. Partial inverse problems for the Sturm-Liouville
equation with deviating argument. Mathematical Methods in the Applied
Sciences, vol.41, no.17 (2018), 8350-8354 (with Bondarenko N.P.).
(182) Yurko V.A. Inverse problems for arbitrary order differential
operators with discontinuties in an interior point. Results in
Mathematics, vol.73, no.1 (2018), paper 25.
(183) Yurko V.A. Inverse problems for arbitrary order integral and
integro-differential operators. Results in Mathematics, vol.73, no.2
(2018), article 72.
(184) Yurko V.A. An inverse spectral problem for Sturm-Liouville operators with a large
constant delay. Analysis and Mathematical Physics, vol.9, no.1 (2019), 17-27.
(with Buterin S.)
(185) Yurko V.A. Inverse problems for second order integral and integro-differential
operators. Analysis and Mathematical Physics, vol.9, no.1 (2019), 555-564
(with Buterin S.A.).
(186) Yurko V.A. Inverse spectral problems for differential pencils on arbitrary compact
graphs. Differ. Uravn., vol.55, no.1 (2019), 25-33; English transl. in Differential
Equations, vol.55, no.1 (2019), 24-33.
(187) Yurko V.A. Recovering differential operators with retarded argument. Differ. Uravn.,
vol.55, no.4 (2019), 524-528; English transl. in Differential Equations, vol.55, no.4
(2019), 510-514.
(188) Yurko V.A. On an inverse problem for differential operators on a finite interval with
complex weights. Mat. Zametki, vol.105, no.2 (2019), 313-320; English transl. in
Mathematical Notes, vol.105, no.2 (2019), 301-306.
(189) Yurko V.A. Estimates of complex eigenvalues and inverse spectral problem for the
transmission eigenvalue problem. Electronic Journal of Qualitative Theory of
Differential Equations, no.38 (2019), 1-15 (with S. Buterin, C-F. Yang, X-C. Xu).
(190) Yurko V.A. An inverse problem for Sturm-Liouville operators on the half-line with
complex weights. Journal of Inverse and Ill-Posed Problems, vol.27 (2019), no.3,
439–443.
(191) Yurko V.A. An inverse spectral problem for second order differential operators
with retarded argument. Results in Mathematics, vol.74, no.2 (2019), article 71, 10pp.
(192) Yurko V.A. The uniqueness in inverse problems for Dirac operators with the
interior twin-dense nodal subset (with Wang Yu Ping and Shieh Chung-Tsun);
Journal of Mathematical Analysis and Applications, vol.479, no.1 (2019), 1383-1402.
(193) Yurko V.A. Inverse problems for Sturm-Liouville differential operators on closed
sets. Tamkang Journal of Mathematics, vol.50, no.3 (2019), 199-206.
(194) Yurko V.A. Inverse spectral problems for differential systems.
Modern Methods in Operator Theory and Harmonic Analysis.
Springer Proceedings in Mathematics and Statistics, Springer, 2019, pp.451-475.
(195) Yurko V.A. Solution of inverse problems for differential operators
with delay. Transmutation operators and Applications. Trends in Mathematics, Springer, 2020, 467-475.
(196) Yurko V.A. Inverse spectral problems for differential operators with non-separated
boundary conditions. Journal Inverse and Ill-Posed Problems, vol.28, no.4 (2020), 567-616.
(197) Yurko V.A. On the Hochstadt-Lieberman problem for the Dirac
operator with discontinuity. Journal of Inverse and Ill-Posed Problems (2020), vol.28, no.6 (2020),
849-855 (with Yang C.F. and Zhang Ran).
(198) Yurko V.A. Inverse problems for differential operators with
indefinite discontinuous weights. Results in Mathematics, vol.75 (2020), Article 138, 13pp.
(199) Yurko V.A. Spectral analysis of higher-order differential operators with
discontinuity conditions at interior points. Journal of Mathematical Sciences,
vol.250, no.4 (2020), 705-715.
(200) Yurko V.A. Direct and inverse problems of spectral analysis for arbitrary order
differential operators with non-integrable regular singularities. Modern Mathematics.
Fundamental Research, vol.67, no.2 (2021), 408-421.
(201) Yurko V.A. On inverse spectral problems for Sturm-Liouville differential
operators on closed sets (with Buterin S.A. and Kuznetsova M.).
Lobachevskii Journal of Mathematics, vol.42, no.6 (2021), 1201-1209.
(202) Yurko V.A. Recovering differential operators on the
half-Line with indefinite discontinuous weights. Tamkang Journal of Mathematics, vol.52, no.1 (2021), 155-169.
(203) Yurko V.A. Inverse problems of recovering first order integro-differential
operators from spectra. Applicable Analysis (2021), 6pp. (with Bondarenko N.P.).
https://doi.org/10.1080/00036811.2021.1932833.
(204) Yurko V.A. A new approach to the inverse discrete transmission eigenvalue problem.
Inverse Problems and Imaging (2021) (with Bondarenko N.P.)
- Over 60 research grants were received from international and Russian funds
