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Pavlenko, Vyacheslav Nikolaevich
Statistics Math-Net.Ru
Total publications: 52
Scientific articles: 49

Number of views:
This page:2654
Abstract pages:13419
Full texts:2909
References:1748
Professor
Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 17.07.1946
E-mail:
Keywords: equatiouns and variational inequalities with discountinuous nonlimarities; nonlinear eigenvalue problems; control problems involving discountinuous nonlimarities. elliptic problem,parabolic problem,discontinuous nonlinearities,semiregular solutions
UDC: 517.948, 517.95, 517.968, 517.97, 517.98, 517.956, 517.988, 517.956.4, 2
MSC: 35J65, 35J85, 35K60, 35P30, 45G10, 47J05, 47J10, 47J20, 47J30, 49J20, 49K27

Subject:

Foundations of the theory of equations with discontinuous nonlinearities are established. This theory includes wide class of elliptic and parabolic boundary-value problems with discontinuous nonlinearities.

Biography

Graduated from Faculty of Mathematica and Mechanica of M. V. Lomonosov Moscow State University (MSU) in 1969 (department of differential equations). Ph. D. thesis was defended in 1972. D. Sci. thesis was defended in 1995. A list of my works contains more than 40 titles.

In 1955, 1997, 1998 I was awarded by grant of International Soros Program of Education in exact sciences in nomination "Soros associate professor". In 2000 and 2001 I entered in number of the winners in competition in nomination "Soros professor".
   
Main publications:
  1. V.N.Pavlenko, “O razreshimosti nekotorykh nelineinykh uravnenii s razryvnymi operatorami”, Dokl. AN SSSR, 204:6 (1972), 1320-1323  mathnet
  2. V.N.Pavlenko,D.K.Potapov, “Suschestvovanie polupravilnykh reshenii ellipticheskikh spektralnykh zadach s razryvnymi nelineinostyami.”, Matematicheskii sbornik, 206:9 (2015), 121-138  mathnet
  3. V.N.Pavlenko, “Variatsionnyi metod dlya uravnenii s razryvnymi operatorami”, Vestnik ChelGU, 1994, № 2, 87-95
  4. V.N.Pavlenko,D.K.Potapov, “Ob odnom klasse ellipticheskikh kraevykh zadach s parametrom i razryvnymi nelineinostyami”, Izvestiya RAN.Seriya matematicheskaya., 84:3 (2020), 168-184  mathnet
  5. V.N.Pavlenko, “Silnye resheniya periodicheskikh parabolicheskikh zadach s razryvnymi nelineinostyami”, Differentsialnye uravneniya, 52:4 (2016), 528-538
  6. Pavlenko V. N., “Teoremy suschestvovaniya dlya ellipticheskikh variatsionnykh neravenstv s kvazipotentsialnymi operatorami”, Differents. uravneniya, 24:8 (1988), 1397–1402  mathnet
  7. Pavlenko V. N., “Upravlenie singulyarnymi raspredelennymi sistemiami parabolicheskogo tipa s razryvnymi nelineinostyami”, Ukr. matem. zhurn., 46:6 (1994), 729–736
  8. Pavlenko V. N., “O suschestvovanii polupravilnykh reshenii pervoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s razryvnoi nelineinostyu”, Differents. uravneniya, 27:3 (1991), 520–526  mathnet
  9. Pavlenko V. N., Vinokur V. V., “Rezonansnye kraevye zadachi dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, Izvestiya vuzov, ser. matem., 2001, № 5(468), 43–58  mathnet
  10. Pavlenko V. N., Potapov D. K., “O suschestvovanii lucha sobstvennykh znachenii dlya uravnenii s razryvnymi operatorami”, Sib. matem. zhurn., 42:4 (2001), 911–919  mathnet

https://www.mathnet.ru/eng/person17956
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/245664

Publications in Math-Net.Ru Citations
2024
1. V. N. Pavlenko, D. K. Potapov, “Semi-regular solutions of integral equations with discontinuous nonlinearities”, Mat. Zametki, 116:1 (2024),  109–121  mathnet; Math. Notes, 116:1 (2024), 93–103
2023
2. V. N. Pavlenko, E. A. Derkunova, “The asymptotic behavior of the approximate solution of a one-dimensional singularly perturbed Goldshtik problem”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 15:4 (2023),  14–20  mathnet
2022
3. S. F. Dolbeeva, V. N. Pavlenko, S. V. Matveev, O. N. Dementiev, E. A. Sbrodova, A. A. Soloviev, V. I. Ukhobotov, V. E. Fedorov, A. A. Ershov, “Arlen Mikhaylovich Il'in. 90 years since the birth”, Chelyab. Fiz.-Mat. Zh., 7:2 (2022),  135–138  mathnet
4. V. N. Pavlenko, D. K. Potapov, “One class of quasilinear elliptic type equations with discontinuous nonlinearities”, Izv. RAN. Ser. Mat., 86:6 (2022),  143–160  mathnet  mathscinet; Izv. Math., 86:6 (2022), 1162–1178  isi  scopus
5. V. N. Pavlenko, D. K. Potapov, “Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth”, Mat. Sb., 213:7 (2022),  121–138  mathnet  mathscinet; Sb. Math., 213:7 (2022), 1004–1019  isi  scopus 1
2021
6. V. N. Pavlenko, D. K. Potapov, “About a problem on conductor heating”, Chelyab. Fiz.-Mat. Zh., 6:3 (2021),  299–311  mathnet
7. V. N. Pavlenko, D. K. Potapov, “Positive solutions of superlinear elliptic problems with discontinuous non-linearities”, Izv. RAN. Ser. Mat., 85:2 (2021),  95–112  mathnet  elib; Izv. Math., 85:2 (2021), 262–278  isi  scopus 2
8. V. N. Pavlenko, D. K. Potapov, “Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities”, Mat. Zametki, 110:2 (2021),  239–257  mathnet  elib; Math. Notes, 110:2 (2021), 226–241  isi  scopus 3
9. V. N. Pavlenko, D. K. Potapov, “Variational method for elliptic systems with discontinuous nonlinearities”, Mat. Sb., 212:5 (2021),  133–152  mathnet  elib; Sb. Math., 212:5 (2021), 726–744  isi  scopus 4
2020
10. V. N. Pavlenko, D. K. Potapov, “On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity”, Izv. RAN. Ser. Mat., 84:3 (2020),  168–184  mathnet  mathscinet  elib; Izv. Math., 84:3 (2020), 592–607  isi  scopus 4
2019
11. V. N. Pavlenko, A. A. Asryan, “Periodic solutions existence for a second order differential equation with a discontinuous nonlinearity”, Chelyab. Fiz.-Mat. Zh., 4:3 (2019),  323–332  mathnet
12. V. N. Pavlenko, E. Yu. Postnikova, “Sturm — Liouville problem for an equation with a discontinuous nonlinearity”, Chelyab. Fiz.-Mat. Zh., 4:2 (2019),  142–154  mathnet  elib 2
13. V. N. Pavlenko, D. K. Potapov, “Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity”, Mat. Sb., 210:7 (2019),  145–170  mathnet  mathscinet  elib; Sb. Math., 210:7 (2019), 1043–1066  isi  scopus 4
2018
14. V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Mat. Zametki, 103:1 (2018),  92–100  mathnet  mathscinet  elib; Math. Notes, 103:1 (2018), 89–95  isi  scopus 7
2017
15. V. N. Pavlenko, D. K. Potapov, “Existence of Three Nontrivial Solutions of an Elliptic Boundary-Value Problem with Discontinuous Nonlinearity in the Case of Strong Resonance”, Mat. Zametki, 101:2 (2017),  247–261  mathnet  mathscinet  elib; Math. Notes, 101:2 (2017), 284–296  isi  scopus 8
16. V. N. Pavlenko, D. K. Potapov, “Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides”, Mat. Sb., 208:1 (2017),  165–182  mathnet  mathscinet  elib; Sb. Math., 208:1 (2017), 157–172  isi  scopus 8
17. V. N. Pavlenko, D. K. Potapov, “Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities”, Sibirsk. Mat. Zh., 58:2 (2017),  375–385  mathnet  elib; Siberian Math. J., 58:2 (2017), 288–295  isi  elib  scopus 5
2016
18. V. N. Pavlenko, D. K. Potapov, “Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity”, Mat. Tr., 19:1 (2016),  91–105  mathnet  mathscinet  elib; Siberian Adv. Math., 27:1 (2017), 16–25  scopus 7
2015
19. V. N. Pavlenko, D. K. Potapov, “The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities”, Mat. Sb., 206:9 (2015),  121–138  mathnet  mathscinet  zmath  elib; Sb. Math., 206:9 (2015), 1281–1298  isi  scopus 13
2012
20. V. N. Pavlenko, T. A. Petrash, “Periodic solutions of the vibrating string equation with Neumann and Dirichlet boundary conditions and a discontinuous nonlinearity”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:2 (2012),  199–204  mathnet  elib 2
21. I. F. Galikhanov, V. N. Pavlenko, “Periodic solutions of the telegraph equation with a discontinuous nonlinearity”, Ufimsk. Mat. Zh., 4:2 (2012),  74–79  mathnet  mathscinet 2
2011
22. V. N. Pavlenko, M. S. Fedyashev, “Periodic solutions of parabolic equations with discontinuous nonlinearities”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14,  94–101  mathnet 1
23. V. N. Pavlenko, D. Y. Medvedev, “Periodic solutions of parabolic equations with homogeneus bondary Dirichlet conditions time depent coefficients and discontinuous nonlinearity”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 13,  20–26  mathnet
2010
24. V. N. Pavlenko, “The resonance elliptic boundary value problem with discontinuous nonlinearity of linear growth”, Vestnik Chelyabinsk. Gos. Univ., 2010, no. 12,  43–48  mathnet
2008
25. V. N. Pavlenko, “Parabolic type equations with discontinuous nonlinearity”, Vestnik Chelyabinsk. Gos. Univ., 2008, no. 10,  49–53  mathnet 1
2006
26. V. N. Pavlenko, M. A. Pribyl, “Resonance elliptic variational inequalities with discontinuous nonlinearities”, Differ. Uravn., 42:1 (2006),  120–125  mathnet  mathscinet; Differ. Equ., 42:1 (2006), 132–138 2
2005
27. M. G. Lepchinski, V. N. Pavlenko, “Proper solutions of elliptic boundary-valus problems with discontinuous nonlinearities”, Algebra i Analiz, 17:3 (2005),  124–138  mathnet  mathscinet  zmath; St. Petersburg Math. J., 17:3 (2006), 465–475 11
28. V. N. Pavlenko, E. A. Chizh, “Strongly resonance elliptic variational inequalities with discontinuous nonlinearities”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 7,  49–56  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 49:7 (2005), 47–54 3
29. V. N. Pavlenko, D. K. Potapov, “Approximation of boundary value problems of elliptic type with a spectral parameter and a discontinuous nonlinearity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 4,  49–55  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 49:4 (2005), 46–52 7
30. M. G. Lepchinski, V. N. Pavlenko, “Approximation of the resonance boundary-value problems of elliptic type with a discontinuous nonlinearity”, Sibirsk. Mat. Zh., 46:1 (2005),  139–148  mathnet  mathscinet  zmath; Siberian Math. J., 46:1 (2005), 111–118  isi 4
2003
31. V. N. Pavlenko, E. A. Chizh, “Регуляризация для уравнений с разрывными некоэрцитивными операторами”, Vestnik Chelyabinsk. Gos. Univ., 2003, no. 9,  111–123  mathnet
32. M. G. Lepchinski, V. N. Pavlenko, “Аппроксимация краевых задач эллиптического типа с разрывной нелинейностью”, Vestnik Chelyabinsk. Gos. Univ., 2003, no. 7,  89–98  mathnet
2002
33. V. N. Pavlenko, O. V. Ul'yanova, “Method of Upper and Lower Solutions for Parabolic-Type Equations with Discontinuous Nonlinearities”, Differ. Uravn., 38:4 (2002),  499–504  mathnet  mathscinet; Differ. Equ., 38:4 (2002), 520–527 15
34. V. N. Pavlenko, L. B. Kozhaeva, “Управление эллиптическими резонансными системами с разрывными нелинейностями”, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6,  147–154  mathnet
35. V. N. Pavlenko, E. A. Chizh, “Задача Дирихле для уравнения Лапласа с разрывной нелинейностью без условия Ландесмана–Лазера”, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6,  120–126  mathnet
36. V. N. Pavlenko, D. K. Potapov, “О существовании полуоси положительных собственных значений для уравнений с разрывными операторами”, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6,  114–119  mathnet
37. V. N. Pavlenko, V. V. Vinokur, “Теоремы существования для уравнений с некоэрцитивными разрывными операторами”, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6,  104–113  mathnet
2001
38. V. N. Pavlenko, V. V. Vinokur, “Resonance boundary value problems for elliptic-type equations with discontinuous nonlinearities”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 5,  43–58  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 45:5 (2001), 40–55 16
39. V. N. Pavlenko, D. K. Potapov, “Existence of a ray of eigenvalues for equations with discontinuous operators”, Sibirsk. Mat. Zh., 42:4 (2001),  911–919  mathnet  mathscinet  zmath; Siberian Math. J., 42:4 (2001), 766–773  isi 43
1999
40. V. N. Pavlenko, “Управление распределенными системами эллиптического типа с разрывными нелинейностями”, Vestnik Chelyabinsk. Gos. Univ., 1999, no. 5,  56–67  mathnet 1
1998
41. V. N. Pavlenko, O. V. Ul'yanova, “The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 11,  69–76  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 42:11 (1998), 65–72 21
1995
42. V. N. Pavlenko, “Control of distributed systems of elliptic type with discontinuous nonlinearities”, Differ. Uravn., 31:9 (1995),  1586–1587  mathnet  zmath 4
1994
43. V. N. Pavlenko, “Вариационный метод для уравнений с разрывными операторами”, Vestnik Chelyabinsk. Gos. Univ., 1994, no. 2,  87–95  mathnet 6
1993
44. V. N. Pavlenko, “The method of monotone operators in problems of the control of distributed systems of elliptic type with discontinuous nonlinearities”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 8,  49–54  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:8 (1993), 47–53 5
1991
45. V. N. Pavlenko, “On the existence of semiregular solutions of the first boundary value problem for an equation of parabolic type with a discontinuous nonmonotone nonlinearity”, Differ. Uravn., 27:3 (1991),  520–526  mathnet  mathscinet; Differ. Equ., 27:3 (1991), 374–379 13
46. V. N. Pavlenko, “The method of monotone operators for equations with discontinuous nonlinearities”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 6,  38–45  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:6 (1991), 38–44 4
47. V. N. Pavlenko, “Эллиптические вариационные неравенства с разрывными полумонотонными операторами”, Vestnik Chelyabinsk. Gos. Univ., 1991, no. 1,  29–36  mathnet
1988
48. V. N. Pavlenko, “Existence theorems for elliptic variational inequalities with quasipotential operators”, Differ. Uravn., 24:8 (1988),  1397–1402  mathnet  mathscinet; Differ. Equ., 24:8 (1988), 913–916 17
1972
49. V. N. Pavlenko, “On the solvability of some nonlinear equations with discontinuous operators”, Dokl. Akad. Nauk SSSR, 204:6 (1972),  1320–1323  mathnet  mathscinet  zmath 6
2022
50. I. V. Bychkov, S. M. Voronin, O. N. Dementiev, V. L. Dilman, V. I. Zalyapin, D. A. Zakharyevich, D. B. Izergin, V. V. Karachik, A. Yu. Makovetskii, L. D. Menikhes, V. N. Pavlenko, M. V. Plekhanova, E. A. Sbrodova, S. V. Taskaev, V. I. Ukhobotov, “Владимир Евгеньевич Федоров. К пятидесятилетию со дня рождения”, Chelyab. Fiz.-Mat. Zh., 7:1 (2022),  5–10  mathnet
2017
51. S. F. Dolbeeva, V. N. Pavlenko, S. V. Matveev, O. N. Dementiev, A. V. Mel'nikov, E. A. Sbrodova, A. A. Soloviev, V. I. Ukhobotov, V. E. Fedorov, E. A. Fominykh, A. A. Ershov, “Arlen Mikhaylovich Il’in. Towards 85th birthday”, Chelyab. Fiz.-Mat. Zh., 2:1 (2017),  5–9  mathnet  elib
52. B. K. Vodolaga, S. A. Zagrebina, A. A. Zamyshlyaeva, A. V. Keller, N. L. Klinacheva, Yu. M. Kovalev, A. N. Kraiko, È. S. Kuropatenko, I. V. Kuropatenko, M. V. Kuropatenko, V. A. Levin, I. R. Makeyeva, N. F. Morozov, V. N. Pavlenko, G. A. Sviridyuk, V. A. Simonenko, V. M. Titov, A. V. Fedorov, N. N. Fedorova, V. M. Fomin, N. A. Fomin, A. L. Shestakov, E. S. Shestakovskaya, “Valentin Fedorovich Kuropatenko (1933–2017)”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:4 (2017),  151–152  mathnet  elib

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