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Pokorny, Yulii Vitaljevich
(1940–2010)
Statistics Math-Net.Ru
Total publications: 68
Scientific articles: 53

Number of views:
This page:4850
Abstract pages:18808
Full texts:9102
References:1130
Professor
Doctor of physico-mathematical sciences (1980)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 6.02.1940
Keywords: differential equations on networks, differentiation and integration with respect to the measure, Green function, multipoint and non-standard boundary value problems, oscillation spectral theorems, Tchebyshev and Markov systems, positive operators in the space with a cone, focusing.

Subject:

Differential equations on networks. The concept of differential equation on network as a special type of differential equation (intermediate between ordinary and partial differential equations), the maximum principle established, the solvability of boundary value problems is investigated, Green function is constructed, the complete analugue of the theory of disconjugacy is developed, and for neworks of tree-type the oscillation structure of the spectrum is proved. Multipoint and non-standard boundary value problems. The estimates of Green function are obtained, the technique of normalising of Green function by the sign-changing weight is developed, oscillation theorems are obtained. Positive operators in the space with a cone. Discovered the property which called later the focusing one, the connection of this property with the estimate of the spectral gap is proved. Tchebyshev and Markov systems. The counterexample to the theorem of M. A. Rutman on integral representation of the Markov system is discovered. To repair the possibility of such representation the technique of the differentiation and integration with respect to the fractional measure is developed. Differentiation and integration with respect to the measure. The technique of the differentiation and integration with respect to the fractional measure applying to the analysis of multipoint discontinupus boundary problems and boundary problems on networks is developed. For equations of the second order with differentiation with respect to the measure the complete analogue of Sturm–Liouville theory is obtained.

Biography

Graduated from Voronezh State University (Mathematical department) in 1961. Candidate (Ph.D.) thesis "On the second solutions of nonlinear equations in the space with a cone" — 1967. Doctor thesis "Problems of the qualitative theory of Vallee–Poussin boundary value problem" — 1981. About 200 papers.

Director of Research Institute of Mathematics attached to Voronezh State University (1986–1998), Honour Scientist of Russian Federation, State Reseach Maitenance for Outstanding Scientists (1997–2000, 2001^ndash;2004), AMS member, fellowship of IBC.
   
Main publications:
  • Pokornyi Yu. V., Krasnoselskii M. A. Nenulevye resheniya uravnenii s silnymi nelineinostyami // Matem.zametki, 1969. T. 5, vyp. 2. S. 253–260.
  • Pokornyi Yu. V., Lazarev K. P. Nekotorye ostsillyatsionnye teoremy dlya mnogotochechnykh zadach // Differents. uravneniya. 1987. T. 23, # 4. S. 658–670.
  • Borovskikh A. V., Pokornyi Yu. V. Sistemy Chebysheva–Khaara v teorii razryvnykh yader Kelloga // Uspekhi matem. nauk. 1994. T. 49, # 3. S. 3–42.
  • Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. O nelineinoi kraevoi zadache na grafe // Differents. uravneniya. 1998. T. 34, # 5. S. 629–637.
  • Pokornyi Yu. V. Integral Stiltesa i proizvodnye po mere v obyknovennykh differentsialnykh uravneniyakh // Dokl. AN. 1999. T. 364, # 2. S. 167–169.

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List of publications on Google Scholar
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https://mathscinet.ams.org/mathscinet/MRAuthorID/209139
https://elibrary.ru/author_items.asp?authorid=3345

Publications in Math-Net.Ru Citations
2009
1. Yu. V. Pokornyi, Zh. I. Bakhtina, “On the Stieltjes Procedure for Closing Gaps in Time Scales”, Mat. Zametki, 86:5 (2009),  733–735  mathnet  mathscinet  zmath  elib; Math. Notes, 86:5 (2009), 690–692  isi  scopus 1
2008
2. Yu. V. Pokornyi, E. V. Gulynina, T. V. Perlovskaya, “The Hicks property for a variational problem on a graph”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10,  48–54  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 52:10 (2008), 40–45
3. Yu. V. Pokornyi, M. B. Zvereva, S. A. Shabrov, “Sturm–Liouville oscillation theory for impulsive problems”, Uspekhi Mat. Nauk, 63:1(379) (2008),  111–154  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:1 (2008), 109–153  isi  elib  scopus 39
4. Yu. V. Pokornyi, “Zeros of the Green's function for the de la Vallée-Poussin problem”, Mat. Sb., 199:6 (2008),  105–136  mathnet  mathscinet  zmath  elib; Sb. Math., 199:6 (2008), 891–921  isi  elib  scopus 9
2007
5. Yu. V. Pokornyi, Zh. I. Bakhtina, A. S. Ishchenko, “On solvability of certain classes of irregular the second order variation problems”, Izv. Saratov Univ. Math. Mech. Inform., 7:2 (2007),  32–36  mathnet 1
6. Yu. V. Pokornyi, M. B. Zvereva, A. S. Ishchenko, S. A. Shabrov, “An Irregular Extension of the Oscillation Theory of the Sturm–Liouville Spectral Problem”, Mat. Zametki, 82:4 (2007),  578–582  mathnet  mathscinet  zmath  elib; Math. Notes, 82:4 (2007), 518–521  isi  scopus 14
7. Yu. V. Pokornyi, I. Yu. Pokornaya, V. L. Pryadiev, N. N. Ryabtseva, “Integration in Variational Inequalities on Spatial Grids”, Mat. Zametki, 81:6 (2007),  904–911  mathnet  mathscinet  zmath  elib; Math. Notes, 81:6 (2007), 810–816  isi  scopus 1
8. Yu. V. Pokornyi, M. B. Zvereva, S. A. Shabrov, “Some questions of the qualitative theory of nonsmooth Sturm-Liouville problems”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007),  255–274  mathnet  mathscinet; J. Math. Sci. (N. Y.), 143:4 (2007), 3342–3354  scopus
2006
9. Yu. V. Pokornyi, E. V. Gulynina, M. B. Zvereva, “The Influence function is Simpler and Better than Green's Function for a Generalized Stieltjes String”, Mat. Zametki, 80:1 (2006),  149–153  mathnet  mathscinet  zmath  elib; Math. Notes, 80:1 (2006), 146–150  isi  scopus
2004
10. Yu. V. Pokornyi, V. L. Pryadiev, “Some problems of the qualitative Sturm–Liouville theory on a spatial network”, Uspekhi Mat. Nauk, 59:3(357) (2004),  115–150  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 59:3 (2004), 515–552  isi  scopus 42
2003
11. Yu. V. Pokornyi, T. V. Beloglazova, E. V. Dikareva, T. V. Perlovskaya, “Green Function for a Locally Interacting System of Ordinary Equations of Different Orders”, Mat. Zametki, 74:1 (2003),  146–149  mathnet  mathscinet  zmath; Math. Notes, 74:1 (2003), 141–143  isi  scopus 6
12. Yu. V. Pokornyi, T. V. Beloglazova, K. P. Lazarev, “On a Class of Ordinary Differential Equations of Various Orders on a Graph”, Mat. Zametki, 73:3 (2003),  469–470  mathnet  mathscinet  zmath; Math. Notes, 73:3 (2003), 440–442  isi  scopus 2
2001
13. Yu. V. Pokorny, “Nonoscillation of Ordinary Differential Equations and Inequalities on Spatial Networks”, Differ. Uravn., 37:5 (2001),  661–671  mathnet  mathscinet; Differ. Equ., 37:5 (2001), 695–705 7
2000
14. A. W. Komarov, O. M. Penkin, Yu. V. Pokornyi, “On the spectrum of a uniform network of strings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, no. 4,  23–27  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 44:4 (2000), 21–25 4
1999
15. Yu. V. Pokornyi, R. Mustafokulov, “On the positivity of the Green function of linear boundary value problems for fourth-order equations on a graph”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 2,  75–82  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 43:2 (1999), 71–78 11
1998
16. O. M. Penkin, Yu. V. Pokorny, “On incompatible inequalities for elliptic equations on stratified sets”, Differ. Uravn., 34:8 (1998),  1107–1113  mathnet  mathscinet; Differ. Equ., 34:8 (1998), 1111–1117 6
17. Yu. V. Pokorny, O. M. Penkin, V. L. Pryadiev, “A nonlinear boundary value problem on a graph”, Differ. Uravn., 34:5 (1998),  629–637  mathnet  mathscinet; Differ. Equ., 34:5 (1998), 631–638 1
18. Yu. V. Pokorny, K. P. Lazarev, T. M. Gareeva, “On the spectral properties of some nonlocal boundary value problems”, Differ. Uravn., 34:1 (1998),  45–49  mathnet  mathscinet; Differ. Equ., 34:1 (1998), 44–48
1997
19. Yu. V. Pokorny, R. Mustafokulov, “On the positive invertibility of some boundary value problems for a fourth-order equation”, Differ. Uravn., 33:10 (1997),  1358–1365  mathnet  mathscinet; Differ. Equ., 33:10 (1997), 1364–1371 7
1996
20. Yu. V. Pokornyi, O. Yu. Litmanovich, V. P. Plaksina, “On multivalued differentials of piecewise-smooth functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 11,  73–84  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:11 (1996), 70–81
21. O. M. Penkin, Yu. V. Pokornyi, “On some qualitative properties of equations on a one-dimensional cell complex”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 11,  57–64  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:11 (1996), 54–61 2
22. Yu. V. Pokornyi, V. L. Pryadiev, A. Al-Obeid, “Oscillation properties of the spectrum of a boundary value problem on a graph”, Mat. Zametki, 60:3 (1996),  468–470  mathnet  mathscinet  zmath; Math. Notes, 60:3 (1996), 351–353  isi 26
23. O. M. Penkin, Yu. V. Pokornyi, “On some qualitative properties of equations on a one-dimensional $CW$-complex”, Mat. Zametki, 59:5 (1996),  777–780  mathnet  mathscinet  zmath; Math. Notes, 59:5 (1996), 562–565  isi 18
1995
24. A. V. Borovskikh, R. Mustafokulov, K. P. Lazarev, Yu. V. Pokorny, “On a class of fourth-order differential equations on a three-dimensional network”, Dokl. Akad. Nauk, 345:6 (1995),  730–732  mathnet  mathscinet  zmath 10
25. Yu. V. Pokorny, “On a quasidifferential equation generated by a continuous Chebyshev system”, Dokl. Akad. Nauk, 345:2 (1995),  171–174  mathnet  mathscinet  zmath
26. A. V. Borovskikh, K. P. Lazarev, Yu. V. Pokornyi, “On the Kellogg kernels in discontinuous problems”, Trudy Mat. Inst. Steklov., 211 (1995),  102–120  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 211 (1995), 92–108 3
1994
27. A. V. Borovskikh, K. P. Lazarev, Yu. V. Pokorny, “Oscillatory spectral properties of discontinuous boundary value problems”, Dokl. Akad. Nauk, 335:4 (1994),  409–412  mathnet  mathscinet  zmath; Dokl. Math., 49:2 (1994), 328–333 4
28. Yu. V. Pokorny, “On an integral representation of Markov systems”, Dokl. Akad. Nauk, 335:1 (1994),  18–20  mathnet  mathscinet  zmath; Dokl. Math., 49:2 (1994), 229–232
29. I. G. Karelina, Yu. V. Pokornyi, “On the Green function for a boundary value problem on a graph”, Differ. Uravn., 30:1 (1994),  41–47  mathnet  mathscinet; Differ. Equ., 30:1 (1994), 35–40 1
30. A. V. Borovskikh, Yu. V. Pokornyi, “Chebyshev–Haar systems in the theory of discontinuous Kellogg kernels”, Uspekhi Mat. Nauk, 49:3(297) (1994),  3–42  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:3 (1994), 1–42  isi 18
1993
31. Yu. V. Pokornyi, A. V. Borovskikh, “On the Kellogg theorem for discontinuous Green functions”, Mat. Zametki, 53:1 (1993),  151–153  mathnet  mathscinet  zmath; Math. Notes, 53:1 (1993), 110–111  isi 2
1991
32. Yu. V. Pokorny, I. G. Karelina, “On the Green function for the Dirichlet problem on a graph”, Dokl. Akad. Nauk SSSR, 318:3 (1991),  542–544  mathnet  mathscinet  zmath; Dokl. Math., 43:3 (1991), 732–734 5
33. Yu. V. Pokornyi, I. G. Karelina, “Nonlinear comparison theorems on graphs”, Mat. Zametki, 50:2 (1991),  155–157  mathnet  mathscinet  zmath; Math. Notes, 50:2 (1991), 879–880  isi
1989
34. Yu. V. Pokorny, O. M. Penkin, “Sturm theorems for equations on graphs”, Dokl. Akad. Nauk SSSR, 309:6 (1989),  1306–1308  mathnet  mathscinet  zmath; Dokl. Math., 40:3 (1990), 640–642 7
35. Yu. V. Pokorny, K. P. Lazarev, T. M. Gareeva, “Conditions of V. A. Il'in type for the solvability of nonlocal boundary value problems for ordinary differential equations”, Dokl. Akad. Nauk SSSR, 304:6 (1989),  1298–1302  mathnet  mathscinet  zmath; Dokl. Math., 39:1 (1989), 210–213
36. Yu. V. Pokornyi, K. P. Lazarev, T. M. Gareeva, “Nonlocal boundary value problems for ordinary differential equations”, Differ. Uravn., 25:8 (1989),  1321–1332  mathnet  mathscinet  zmath; Differ. Equ., 25:8 (1989), 936–945
37. Yu. V. Pokornyi, O. M. Penkin, “Comparison theorems for equations on graphs”, Differ. Uravn., 25:7 (1989),  1141–1150  mathnet  mathscinet; Differ. Equ., 25:7 (1989), 802–809 10
38. Yu. V. Pokornyĭ, I. Yu. Shurupova, “The Green function of a quasi-interpolation multipoint problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, no. 9,  46–52  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:9 (1989), 46–51
1988
39. O. M. Penkin, Yu. V. Pokornyi, “On a boundary value problem on a graph”, Differ. Uravn., 24:4 (1988),  701–703  mathnet  mathscinet  zmath 6
40. Yu. V. Pokornyi, “An oscillation theorem of S. N. Bernshtein”, Mat. Zametki, 43:5 (1988),  615–623  mathnet  mathscinet  zmath; Math. Notes, 43:5 (1988), 355–359  isi
1987
41. S. V. Meleshko, Yu. V. Pokornyi, “On a vibrational boundary value problem”, Differ. Uravn., 23:8 (1987),  1466–1467  mathnet  zmath 2
42. Yu. V. Pokornyi, K. P. Lazarev, “Some oscillation theorems for multipoint problems”, Differ. Uravn., 23:4 (1987),  658–670  mathnet  mathscinet 14
1978
43. Yu. V. Pokorny, “Distribution of zeros of $T$-extensions”, Dokl. Akad. Nauk SSSR, 239:6 (1978),  1298–1301  mathnet  mathscinet  zmath
44. Yu. V. Pokornyi, “A nonclassical de la Vallée Poussin problem”, Differ. Uravn., 14:6 (1978),  1018–1027  mathnet  mathscinet  zmath 7
1977
45. Yu. V. Pokornyi, “Some estimates of differentiable functions”, Mat. Zametki, 21:5 (1977),  653–664  mathnet  mathscinet  zmath; Math. Notes, 21:5 (1977), 366–373
46. Yu. V. Pokornyi, “The spectrum of an interpolational boundary value problem”, Uspekhi Mat. Nauk, 32:6(198) (1977),  263–264  mathnet  mathscinet  zmath 3
1976
47. Yu. V. Pokornyi, S. V. Smitskikh, “Inversion of the oscillatory property of focusing operators”, Mat. Zametki, 20:5 (1976),  753–760  mathnet  mathscinet  zmath; Math. Notes, 20:5 (1976), 980–984
1975
48. Yu. V. Pokornyi, “Second solutions of multipoint boundary value problems with convex nonlinearities”, Differ. Uravn., 11:10 (1975),  1801–1810  mathnet  mathscinet  zmath 1
1971
49. P. P. Zabreiko, M. A. Krasnosel'skii, Yu. V. Pokornyi, “On a class of linear positive operators”, Funktsional. Anal. i Prilozhen., 5:4 (1971),  9–17  mathnet  mathscinet  zmath; Funct. Anal. Appl., 5:4 (1971), 272–279 16
50. Yu. V. Pokornyi, “Inequality for second characteristic values of positive operators of certain classes”, Mat. Zametki, 9:1 (1971),  27–33  mathnet  mathscinet  zmath; Math. Notes, 9:1 (1971), 17–20 3
1970
51. Yu. V. Pokornyi, “Second solutions of the nonlinear de la Vallée Poussin problem”, Differ. Uravn., 6:9 (1970),  1599–1605  mathnet  mathscinet  zmath 1
1969
52. M. A. Krasnosel'skii, Yu. V. Pokornyi, “Non-zero solutions of equations with strong nonlinearities”, Mat. Zametki, 5:2 (1969),  253–260  mathnet  mathscinet  zmath; Math. Notes, 5:2 (1969), 153–157 6
1968
53. Yu. V. Pokornyi, “On estimates for the Green's function for a multipoint boundary problem”, Mat. Zametki, 4:5 (1968),  533–540  mathnet  mathscinet  zmath; Math. Notes, 4:5 (1968), 810–814 8
2008
54. Yu. V. Pokornyi, N. V. Titova, “Should one Study Higher Mathematics?”, Math. Ed., 2008, no. 3(47),  50–55  mathnet
2005
55. P. L. Ul'yanov, Yu. V. Pokornyi, S. A. Shabrov, “Voronezh Winter Mathematical School “Modern Methods in Theory of Functions and Adjacent Problems””, Uspekhi Mat. Nauk, 60:3(363) (2005),  185–186  mathnet  elib 1
2003
56. V. A. Il'in, Yu. V. Pokorny, A. V. Borovskikh, “Pontryagin Readings-XIV at Voronezh Spring Mathematical School “Modern Methods in Qualitative Theory of Boundary Value Problems””, Differ. Uravn., 39:11 (2003),  1574  mathnet; Differ. Equ., 39:11 (2003), 1661–1662 4
57. P. L. Ul'yanov, Yu. V. Pokornyi, A. V. Borovskikh, “Contemporary methods in theory of functions and adjacent problems”, Uspekhi Mat. Nauk, 58:4(352) (2003),  177–178  mathnet  mathscinet 1
2001
58. Yu. V. Pokornyi, P. L. Ul'yanov, A. V. Borovskikh, “Voronezh Winter Mathematical School “Modern Methods in Theory of Functions and Adjacent Problems””, Uspekhi Mat. Nauk, 56:4(340) (2001),  185–186  mathnet 2
2000
59. P. L. Ul'yanov, Yu. V. Pokornyi, A. V. Borovskikh, ““Modern Methods in Theory of Functions and Adjacent Problems” on Voronezh Winter Mathematical School”, Uspekhi Mat. Nauk, 55:2(332) (2000),  189–190  mathnet 1
1998
60. E. A. Asarin, I. A. Bakhtin, N. A. Bobylev, V. A. Bondarenko, V. Sh. Burd, E. A. Gorin, S. V. Emel'yanov, P. P. Zabreiko, L. A. Ivanov, V. S. Kozyakin, A. M. Krasnosel'skii, N. A. Kuznetsov, A. B. Kurzhanskii, A. Yu. Levin, È. M. Muhamadiev, A. I. Perov, Yu. V. Pokornyi, A. V. Pokrovskii, D. I. Rachinskii, V. V. Strygin, Ya. Z. Tsypkin, V. V. Chernorutski, “Memory of M. A. Krasnosel'skii”, Avtomat. i Telemekh., 1998, no. 2,  179–184  mathnet
1997
61. V. V. Gusev, Yu. V. Pokornyi, P. L. Ul'yanov, “Contemporary methods in theory of functions and adjacent problems”, Uspekhi Mat. Nauk, 52:4(316) (1997),  251–252  mathnet 1
1995
62. V. A. Il'in, S. M. Nikol'skii, Yu. V. Pokornyi, “Воронежская международная весенняя математическая школа «Понтрягинские чтения-V» (25–29 апреля 1994 г.)”, Differ. Uravn., 31:1 (1995),  178  mathnet
63. Yu. V. Pokornyi, P. L. Ul'yanov, “School “Contemporary methods in theory of functions and adjacent problems of mathematics and mechanics””, Uspekhi Mat. Nauk, 50:4(304) (1995),  187–188  mathnet 1
1994
64. V. A. Il'in, S. A. Lomov, M. S. Nikol'skii, Yu. V. Pokornyi, “«Понтрягинские чтения-IV» на весенней Воронежской математической школе”, Differ. Uravn., 30:3 (1994),  538–539  mathnet
1993
65. P. L. Ul'yanov, Yu. V. Pokornyi, “Voronezh Mathematical School “Theory of Functions, Differential Equations in Mathematical Modelling””, Uspekhi Mat. Nauk, 48:4(292) (1993),  253–254  mathnet 1
1992
66. V. A. Il'in, S. A. Lomov, Yu. V. Pokornyi, “Воронежская весенняя математическая школа «Современные методы качественной теории краевых задач»”, Differ. Uravn., 28:12 (1992),  2191  mathnet
67. V. A. Il'in, S. A. Lomov, Yu. V. Pokornyi, “Воронежская весенняя математическая школа «Современные методы качественной теории краевых задач»”, Differ. Uravn., 28:6 (1992),  1093–1094  mathnet
68. S. M. Nikol'skii, Yu. V. Pokornyi, P. L. Ul'yanov, “Voronezh Winter Mathematical School “Modern Methods in Theory of Functions and Theory of Differential Equations””, Uspekhi Mat. Nauk, 47:1(283) (1992),  227–228  mathnet 3

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