Symbol of department Mathematics and Mechanics Department of Saratov State University
Contacts

chair of Mathematical Physics and Numerical Analysis

Yurko Vyacheslav Anatolevich

Yurko Vyacheslav Anatolevich

Name: Yurko, Vjacheslav

Date of Birth: 28 August 1949

Place of work: Department of Mathematics, Saratov University, Saratov, Russia

Present Position: Professor in Mathematics, Head of the Chair of Mathematical Physics and Numerical Analysis

Institution address: Department of Mathematics, Saratov University, Astrakhanskaya 83, Saratov 410012, Russia

E-mail: yurkova at info.sgu.ru slavayurko at yahoo.com

Office telephone: +7 8452 515538

Field of Science: Mathematics

Fellowships: Russian Academy of Natural Sciences

Research Interests: Differential Equations, Mathematical Physics, Spectral Theory, Inverse Problems

SCIENTIFIC EMPLOYMENT

  1. Assistant Professor, Saratov Polytechnical Institute, Saratov, Russia, 1974-1977.
  2. Associate Professor (Docent), Saratov University, Saratov, Russia, 1977-1991.
  3. Professor, Head of the Ghair of Mathematical Physics and Numerical Analysis, Saratov University, Saratov, Russia, 1991-present

DEGREES

  1. University Diploma in Mathematics, 1971, Saratov State University, Russia.
  2. Kandidat of Sciences in Mathematics and Physics (Ph.D.), 1975, Saratov State University, Russia.
  3. Doctor of Sciences in Mathematics and Physics, 1992, Moscow State University, Russia.

Courses Taught

  • Mathematical Physics;
  • Differential Equations;
  • Functional Analysis;
  • Mathematical Models in Natural Sciences;
  • Numerical Analysis;
  • Special Courses.

BIOGRAPHY

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 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 & integral equations, mathematical physics, inverse problems. The first thesis of V.A. Yurko (for the Kandidat of Science degree, 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.

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 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.

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, spectral theory of differential operators on spatial networks 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 300 research articles and 7 monographs. He has received over 40 research grants from international and Russian funds including grants from Russian Foundation for Basic Research, grants from Russian Ministry of Education, Volkswagen Foundation Grant, Leonard Euler Grants; grants from ISF, DAAD, DFG, Tubitak, ISAAC, NSC, QNRF and other research funds. Prof. Yurko is a Fellow of Russian Academy of Natural Sciences and American Mathematical Society.

Main Publications:

    Main monographs:

  1. Yurko V.A. Inverse Spectral Problems for Differential Operators and their Applications. Gordon and Breach, Amsterdam, 2000, 253pp.
  2. Yurko V.A. Inverse Sturm-Liouville Problems and their Applications, NOVA Science Publishers, New York, 2001, 305pp. (with Freiling G.).
  3. Yurko V.A. Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002, 303pp.
  4. Yurko V.A. Introduction to the theory of inverse spectral problems. Moscow, Fizmatlit, 2007, 384pp. (Russian).
  5. Yurko V.A. Lectures on Differential Equations of Mathematical Physics. NOVA Science Publishers, New York, 2008 (with Freiling G.).
  6. Main research papers:

  7. Yurko V.A. An inverse problem for second order differential operators with regular boundary conditions. Mat. Zametki, 18, no.4 (1975), 569-576 (Russian); English transl. in Math.Notes, 18, no.3-4 (1975), 928-932.
  8. Yurko V.A. Reconstruction of fourth-order differential operators. Diff. Uravneniya, 19, no.11 (1983), 2016-2017. (Russian)
  9. Yurko V.A. Boundary value problems with a parameter in the boundary conditions. Izv. Akad. Nauk Armyan. SSR, Ser. Mat., 19, no.5 (1984), 398-409 (Russian); English transl. in Soviet J. Contemporary Math. Anal., 19, no.5 (1984), 62-73.
  10. Yurko V.A. An inverse problem for integral operators. Mat. Zametki, 37, no.5 (1985), 690-701 (Russian); English transl. in Math. Notes, 37, no.5-6 (1985), 378-385.
  11. Yurko V.A. Uniqueness of the reconstruction of binomial differential operators from two spectra, Mat. Zametki, 43, no.3 (1988), 356-364; English transl. in Math. Notes, 43, no.3-4 (1988), 205-210.
  12. Yurko V.A. Reconstruction of higher-order differential operators. Diff. Uravneniya, 25, no.9 (1989), 1540-1550 (Russian); English transl. in Diff. Equations, 25, no.9 (1989), 1082-1091.
  13. Yurko V.A. Inverse Problem for Differential Operators, Saratov University, Saratov, 1989 (Russian).
  14. Yurko V.A. Recovery of differential operators from the Weyl matrix. Doklady Akad. Nauk SSSR, 313, no.6 (1990), 1368-1372 (Russian); English transl. in Soviet Math. Dokl., 42, no.1 (1991), 229-233.
  15. Yurko V.A. A problem in elasticity theory. Prikladnaya Matematika i Mekhanika, 54, no.6 (1990), 998-1002 (Russian); English transl. in J. Appl. Math. Mech., 54, no.6 (1990), 820-824.
  16. Yurko V.A. An inverse problem for integro-differential operators. Mat. zametki, 50, no.5 (1991), 134-146 (Russian); English transl. in Math. Notes, 50, no.5-6 (1991), 1188-1197.
  17. Yurko V.A. Integration of the Boussinesq equation on the half-line. Diff. Uravneniya 27, no.9 (1991), 1647-1648 (Russian).
  18. Yurko V.A. An inverse problem for differential operators on the half-line. Izv. Vysshikh Uchebnykh Zavedenii, Ser. Mat., no.12 (1991), 67-76 (Russian); English transl. in Soviet Math. (Iz.VVZ), 35, no.12 (1991), 67-74.
  19. Yurko V.A. Solution of the Boussinesq equation on the half-line by the inverse problem method, Inverse Problems, 7 (1991), 727-738.
  20. Yurko V.A. On determination of differential operators on the half-line, Doklady Akad. Nauk Ukrainy, no.9 (1991), 34-37 (Russian).
  21. Yurko V.A. Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix. Mat. Sbornik, 182, no.3 (1991), 431-456 (Russian); English transl. in Math. USSR Sbornik, 72, no.2 (1992), 413-438.
  22. Yurko V.A. Inverse problem for differential equations with a singularity. Diff. Uravneniya, 28, no.8 (1992), 1355-1362 (Russian); English transl. in Diff. Equations, 28 (1992), 1100-1107.
  23. Yurko V.A. On higher-order differential operators with a singular point, Inverse Problems, 9 (1993), 495-502.
  24. Yurko V.A. Inverse problem for selfadjoint differential operators on the half-line. Doklady RAN, 333, no.4 (1993), 449-451 (Russian); English transl. in Russian Acad. Sci Dokl. Math. 48, no.3 (1994), 583-587.
  25. 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 (Russian); English transl. in J. Russ. Math. 37, no.7 (1993), 58-66.
  26. Yurko V.A. On differential operators with nonseparated boundary conditions. Funkt. Analiz i Prilozh., 28, no.4 (1994), 90-92 (Russian); English transl. in Funct. Anal. and Appl., 28, no.4 (1994), 295-297.
  27. Yurko V.A. On determination of selfadjoint differential operators on the half-line, Mat. Zametki, 57, no.3 (1995), 451-462 (Russian); English transl. in Math. Notes, 57, no.3-4 (1995), 310-318.
  28. Yurko V.A. On higher-order differential operators with a singularity. Mat. Sbornik, 186, no.6 (1995), 133-160 (Russian); English transl. in Sbornik; Mathematics 186, no.6 (1995), 901-928.
  29. Yurko V.A. On integration of nonlinear dynamical systems by the inverse problem method. Mat. Zametki, 57, no.6 (1995), 945-949 (Russian); English transl. in Math. Notes, 57, no.6 (1995), 672-675.
  30. Yurko V.A. On higher-order difference operators. J. Difference Equations and Appl., 1 (1995), 347-352.
  31. Yurko V.A. On inverse problems for nonlinear differential equations. Diff. Uravneniya, 31, no.10 (1995), 1768-1769 (Russian); English transl.in Diff. Equations, 31, no.10 (1995), 1741-1743.
  32. 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.).
  33. Yurko V.A. Boundary value problems for a differential equation with a singularity. Doklady Akad. Nauk, 349, no.4 (1996), 460-462 (Russian); English transl. in Doklady Mathematics, 54, no.1 (1996), 571-573.
  34. Yurko V.A. On discrete operators of higher order. Uspekhi Mat. Nauk, 51, no.3 (1996), 217-218 (Russian); English transl.in Russian Math. Surveys, 51, no.3 (1996), 578-580.
  35. Yurko V.A. An inverse problems for operators of a triangular structure. Results in Mathematics, 30, no.3/4 (1996), 346-373.
  36. Yurko V.A. An inverse problem for systems of differential equations with nonlinear dependence on the spectral parameter. Diff. Uravneniya, 33, no.3 (1997), 390-395 (Russian); English transl. in Diff. Equations 33, no.3 (1997), 388-394.
  37. Yurko V.A. Integral transforms connected with differential operators having singularities inside the interval. Integral Transforms and Special Functions, 5, no.3-4 (1997), 309-322.
  38. Yurko V.A. Inverse problems for differential equations with turning points. Inverse Problems, 13 (1997), 1247-1263 (with Freiling G.).
  39. Yurko V.A. On recovering Sturm-Liouville differential operators with singularities inside the interval. Mat. Zametki, 64, no.1 (1998), 143-156 (Russian); English transl. in Math. Notes, 64, no.1 (1998), 121-132.
  40. Yurko V.A. Expansion theorems for boundary value problems with a singularity. Analysis, 18 (1998), 25-39 (with Freiling G.).
  41. Yurko V.A. On constructing differential equations with singularities from incomplete spectral information, Inverse Problems, 14 (1998), 1131-1150 (with Freiling G.).
  42. Yurko V.A. Integrable dynamical systems connected with higher-order difference operators. Izv. Vysshikh Uchebnykh Zavedenii, Ser. Mat., no.10 (1998), 71-81; translation in Russian Math. (Izv. VUZ) 42 (1998), no.10, 69-79.
  43. Yurko V.A. Inverse spectral problems for differential equations on the half-line with turning points, J. Diff. Equations, 154 (1999), 419-453 (with Freiling G.).
  44. Yurko V.A. Reconstructing parameters of a medium from incomplete spectral information, Results in Mathematics 35 (1999), 228-249 (with Freiling G.).
  45. 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.
  46. Yurko V.A. An inverse problem for differential equations of the Orr-Sommerfeld type. Mathematishe Nachrichten, 211 (2000), 177-183.
  47. Yurko V.A. Integral transforms connected with discontinuous boundary value problems, Integral Transforms and Special Functions, vol.10, no.2 (2000), 141-164.
  48. Yurko V.A. On recovery of pencils of differential operators on the half-line, Matemat. Zametki, vol. 67, no. 2 (2000), 316-319 (Russian); English transl.in Math. Notes, 67 (2000), no. 2, 261-265.
  49. Yurko V.A. On boundary value problems with jump conditions inside the interval. Differ. Uravn. 36 (2000), no.8, 1139-1140 (Russian); English transl. in Diff. Equations, (2000), no. 8, 1266-1269.
  50. Yurko V.A. Inverse spectral problems for differential operators and their applications. J. Math. Sciences (New York) 98 (2000), no. 3, 319-426.
  51. Yurko V.A. The inverse spectral problem for differential operators with nonseparated boundary conditions. J. Math. Anal. Appl. 250 (2000), 266-289.
  52. Yurko V.A. An inverse problem for pencils of differential operators. Mat. Sbornik 191 (2000), no. 10, 137-160 (Russian); English transl. in Sbornik: Mathematics 191 (2000), no. 10, 1561-1586.
  53. Yurko V.A. Recovery of differential equations with nonlinear dependence on the spectral parameter, Appl. Anal. 78, no. 1-2 (2001), 63-77.
  54. Yurko V.A. Inverse Spectral Problems and their Applications, Saratov, PI Press, 2001, 499pp. (Russian).
  55. Yurko V.A. On higher-order differential operators with a singularity inside the interval, Matemat. Zametki 71, no.1 (2002) 152-156 (Russian); English transl. in Math. Notes 71 (2002).
  56. Yurko V.A. On the determination of differential equations with singularities and turning points. Results in Mathematics 41 (2002), 275-290 (with Freiling G.).
  57. Yurko V.A. Inverse spectral problems for singular non-selfadjoint differential operators with discontinuties in an interior point. Inverse Problems 18 (2002), 757-773 (with Freiling G.).
  58. Yurko V.A. On recovering singular non-selfadjoint differential operators with a singularity inside the interval, Differen. Uravn. 38, no.5 (2002), 645-659 (Russian); English transl. in Differen. Equations 38, no.5 (2002), 678-694.
  59. Yurko V.A. Integral transforms connected with higher-order differential operators with a singularity, Integral Transforms and Special Functions 13, no.6 (2002), 497-511.
  60. Yurko V.A. Inverse spectral problems for higher-order differential operators with a singularity, Journal of Inverse and Ill-Posed Problems 10, no.4 (2002), 413-425.
  61. Yurko V.A. Higher-order differential equations having a singularity in an interior point, Results in Mathematics (2002) 177-191.
  62. Freiling G, Rykhlov V. and Yurko V., Spectral analysis for an indefinite singular Sturm-Liouville problem, Applicable Analysis 81, no. 6 (2002), 1283-1305.
  63. Yurko V. Half-range expansions for an astrophysical problem, Letters in Mathematical Physics 64 (2003), 65-73 (with Freiling G. and Vietri M.).
  64. Yurko V.A. Spectral analysis for differential operators with singularities. Abstract and Applied Analysis, vol. 2004 (9), no.2 (2004), 165-182.
  65. Yurko V.A. On recovering non-selfadjoint differential systems on the half-line from the Weyl matrix. Matemat. Zametki 76, no.2 (2004), 316-320; (Russian); English transl. in Math. Notes 76, no.2 (2004), 296-302.
  66. 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 396, no.6 (2004), 755-758 (Russian); English transl. in Doklady Mathematics 69, no.3 (2004), 465-468.
  67. Yurko V.A. The inverse problem method on the half-line and a nested system of Riccati equations, Results in Math. 45, no.3-4 (2004), 246-253 (with Freiling G.).
  68. Yurko V.A. An inverse spectral problem for singular non-selfadjoint differential systems. Mat. Sbornik 195, no. 12 (2004), 123-156 (Russian); English transl. in Sbornik: Mathematics 195, no.12 (2004).
  69. Yurko V.A. An inverse problem of spectral analysis for differential systems on the half-line. Mathematica Balkanica 19, no. 1-2 (2005), 233-240.
  70. Yurko V.A. Boundary value problems with regular singularities and singular boundary conditions. Inter. Journal of Math. Math. Sci. vol. 2005, no.9 (2005), 1481-1495 (with Freiling G.).
  71. Yurko V.A. The Weyl-type matrix and the method of spectral mappings in the inverse problem theory. Far East J. of Applied Math. 19, no.2 (2005), 125-146 (with Freiling G.).
  72. 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.).
  73. 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. 41, no.6 (2005), 781-786; English transl. in Diff. Equations 41, no.6 (2005), 818-823.
  74. Yurko V.A. An inverse problem for differential systems with multiplied roots of the characteristic polynomial. Journal of Inverse and Ill-Posed Problems 13, no.5 (2005), 503-512.
  75. Yurko V.A. Inverse spectral problems for Sturm-Liouville operators on graphs. Inverse Problems 21 (2005), 1075-1086.
  76. Yurko V.A. Inverse spectral problems for differential systems on a finite interval. Results in Math. 48, no.3/4 (2005), 371-386.
  77. Yurko V.A. Inverse problems for matrix Sturm-Liouville operators. Russian J. Math. Phys. 13, no.1 (2006), 111-118.
  78. Yurko V.A. On recovering Sturm-Liouville operators on graphs. Matem. Zametki 79, no.4 (2006), 619-630 (Russian); English transl. in Math. Notes 79, no.4 (2006), 572-582.
  79. Yurko V.A. The inverse problem for pencils of differential operators on the half-line with turning points. Fund. Prikl. Mat. 12, no.5 (2006), 237-246 (Russian).
  80. Yurko V.A. An inverse problems for the matrix Sturm-Liouville equation on a finite interval. Inverse Problems 22 (2006), 1139-1149.
  81. Yurko V.A. Inverse spectral problems for differential pencils on the half-line with turning points. J. Math. Anal. Appl. 320 (2006), 439-463.
  82. Yurko V.A. On recovering differential systems on a finite interval from spectra. Trudy MIRAN Steklov, 255 (2006), 273-287; English transl. in Proceedings of the Steklov Institute of Mathematics 255 (2006),260-274.
  83. Yurko V.A. An inverse problem for higher-order differential operators on star-type graphs, Inverse Problems 23 (2007), 893-903.
  84. Yurko V.A. Inverse problems for differential operators on graphs with general matching conditions, Applicable Analysis 86, no.6 (2007), 653-667 (with Freiling G.).
  85. Yurko V.A. Inverse spectral problems for Sturm-Liouville operators on noncompact trees, Results in Mathematics 50 (2007), 195-212 (with Freiling G.).
  86. 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 15, no.8 (2007), 785-798 (with Freiling G.).
  87. Yurko V.A. A numerical algorithm for solving inverse problems for singular Sturm-Liouville operators, Advances in Dynamical Systems and Appl. 2, no.1 (2007), 95-105 (with Freiling G. and Mazur T.).
  88. Yurko V.A. Recovering higher-order differential operators on star-type graphs from spectra. Cubo Mathematical Journal, vol.10, no.1 (2008), 93-102.
  89. Yurko V.A. The inverse problem for pencils of differential operators on the half-line with turning points. Journal of Mathematical Sciences, 150, no.6 (2008), 2620-2627.
  90. Yurko V.A. Numerical methods for solving inverse Sturm-Liouville problems. Results in Mathematics, 52, no.1-2 (2008), 63-74 (with Ignatiev M.Yu.).
  91. Yurko V.A. Inverse problems for Sturm-Liouville operators on graphs with a cycle. Operators and Matrices, vol.2, no.4 (2008), 543-553.
  92. Yurko V.A. Inverse spectral and nodal problems for discontinuous boundary value problems. Journal of Mathematical Analysis and Applications, 347, no.1 (2008), 266-272 (with Chung-Tsun Shieh).
  93. Yurko V.A. Inverse nodal and inverse spectral problems for differential operators on graphs. Journal of Inverse and Ill-Posed Problems 16, no.7 (2008), 715-722.
  94. Yurko V.A. Recovering differential pencils on compact graphs. Journal of Differential Equations, 244 (2008), 431-443.
  95. Yurko V.A. Reconstruction of higher-order differential operators on compact graphs. Doklady Akad. Nauk 419, no.5 (2008), 604-608; English transl: Doklady Mathematics 77, no.2 (2008), 293-297.
  96. Yurko V.A. Inverse problems for differential of any order on trees. Matemat. Zametki 83,no.1 (2008), 139-152; English transl. in Math. Notes 83, no.1 (2008), 125-137.
  97. Yurko V.A. An inverse spectral problem for pencils of differential operators on noncompact networks. Differ. Uravnen. 44, no.12 (2008), 1658-1666; English transl. in Diff. Equations 44, no.12 (2008).
  98. Yurko V.A. 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.).
  99. Yurko V.A. On an inverse spectral problem for differential operators on a hedgehog-type graph. Doklady Akad. Nauk 425, no.4 (2009), 466-470; English transl: Doklady Mathematics 79, no.2 (2009), 250-254.
  100. Yurko V.A. Inverse nodal problems for Sturm-Liouville differential operators on a star-type graph. Sibir. Mat. Zh. 50, no.2 (2009), 467-473; English transl: Siberian Math. Journal 50, no.2 (2009), 373-378.
  101. Yurko V.A. Uniqueness of recovering Sturm-Liouville operators on A-graphs from spectra. Results in Mathematics 55, no.1-2 (2009), 199-207.
  102. Yurko V.A. Inverse spectral problems for differential operators on a graph with a rooted cycle. Tamkang J. Math. 40, no.3 (2009), 271-286.
  103. Yurko V.A. Inverse spectral problems for Sturm-Liouville differential operators on a finite interval. Journal of Inverse and Ill-Posed Proplems. 17 (2009), 639-694.
  104. Yurko V.A. Recovering Sturm-Liouville operators from spectra on a graph with a cycle. Matem. Sbornik 200, no. 9 (2009), 147-160; English transl. in Sbornik: Mathematics 200, no. 9 (2009), 1403-1415.
  105. Yurko V.A. Inverse problems for Sturm-Liouville operators on bush-type graphs. Inverse Problems 25, no.10 (2009), 105008, 14pp.
  106. Yurko V.A. Uniqueness of recovering differential operators on hedgehog-type graphs. Advances in Dynamical Systems and Appl. vol.4, no.2 (2009), 231-241.
  107. Yurko V.A. Inverse nodal problems for differential operators on graphs with a cycle. Tamkang J. Math. 41, no.1 (2010), 15-54 (with Freiling G.).
  108. Yurko V.A. A remark on inverse problems for Sturm-Liouville operators on graphs. Results in Math. (2010), DOI 10.1007/s00025-009-0011-y.
  109. Yurko V.A. An inverse problem for Sturm-Liouville operators on arbitrary compact spatial networks. Doklady Akad. Nauk 432, no.3 (2010), 318-321; English transl: Doklady Mathematics 81, no.3 (2010), 410-413.
  110. Yurko V.A. Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter Inverse Problems 26, N 5 (2010), 055003, 17pp. (with Freiling G.)
  111. Yurko V.A. An inverse problem for Sturm-Liouville operators on A-graphs. // Applied Math. Lett. 23, no.8 (2010), 875-879. DOI 10.1016/j.aml.2010.03.026
  112. Yurko V.A. Inverse spectral problems for differential operators on arbitrary compact graphs. Journal of Inverse and Ill-Posed Proplems 18, no.3 (2010), 245-261.
  113. Yurko V.A. Recovering Sturm-Liouville differential operators on A-graphs. Differen. Uravn. 47, no.1 (2010).
  114. Yurko V.A. Recovering singular differential operators on noncompact star-type graphs from Weyl functions. Tamkang J. Math. 42, no. 2 (2011).

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