Geodesic
Periodic solutions of parabolic equations with homogeneus bondary Dirichlet conditions time depent coefficients and discontinuous nonlinearity
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 13 (2011), pp. 20-26 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The theorem of existence strong periodic solution of parabolic equations with discontinuous unbounded nonlinearity that in accord with homogeneus boundary Dirichlet conditions prove with topological method. Here coefficients of the linear part of the equation are time dependent.
Keywords: periodic solution, resonance problem, discontinuous nonlinearity.
Mots-clés : parabolic equations 
@article{VCHGU_2011_13_a1,
     author = {V. N. Pavlenko and D. Y. Medvedev},
     title = {Periodic solutions of parabolic equations with homogeneus bondary {Dirichlet} conditions time depent coefficients and discontinuous nonlinearity},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {20--26},
     year = {2011},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a1/}
}
TY  - JOUR
AU  - V. N. Pavlenko
AU  - D. Y. Medvedev
TI  - Periodic solutions of parabolic equations with homogeneus bondary Dirichlet conditions time depent coefficients and discontinuous nonlinearity
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2011
SP  - 20
EP  - 26
IS  - 13
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a1/
LA  - ru
ID  - VCHGU_2011_13_a1
ER  - 
%0 Journal Article
%A V. N. Pavlenko
%A D. Y. Medvedev
%T Periodic solutions of parabolic equations with homogeneus bondary Dirichlet conditions time depent coefficients and discontinuous nonlinearity
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2011
%P 20-26
%N 13
%U http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a1/
%G ru
%F VCHGU_2011_13_a1
V. N. Pavlenko; D. Y. Medvedev. Periodic solutions of parabolic equations with homogeneus bondary Dirichlet conditions time depent coefficients and discontinuous nonlinearity. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 13 (2011), pp. 20-26. http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a1/

[1] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[2] M. A. Krasnoselskii, A. V. Pokrovskii, Sistemy s gisterezisom, Nauka, M., 1983, 272 pp. | MR

[3] C. De Coster, P. Omari, “Unstable periodic solutions of a parabolic problem in the presence of non-well-ordered lower and upper solutions”, J. of functional Anal, 175 (2000), 52–88 | DOI | MR | Zbl

[4] Yu. S. Kolesov, “Ob odnom priznake suschestvovaniya periodicheskikh reshenii u parabolicheskikh uravnenii”, DAN SSSR, 170:5 (1966), 1013–1015 | Zbl

[5] H. Amann, “Periodic solution of semilimar parabolic equations”, Nonlinear Analysis. A collection of papers in honor of E. Rothe, Academic press, New York, 1978, 1–29 | MR

[6] I. I. Shmulev, “Periodicheskie resheniya pervoi kraevoi zadachi dlya parabolicheskikh uravnenii”, Matematicheskii sbornik, 66(108):3 (1965), 398–410 | MR | Zbl

[7] A. Castro, A. C. Lazer, “Results on periodic solutions of parabolic equations suggested by elliptic theory”, Bulletino U.M.I., 1.B (1982), 1089–1104 | MR | Zbl

[8] H. Brezis, L. Nirenberg, “Characterizations of the ranges of some nonlinear operators and applications to boundary value problems”, Ann. Scuola Norm. Pisa, 5:2 (1978), 225–325 | MR

[9] E. N. Dancer, P. Hess, “On stable solutions of quasilinear periodic — parabolic problems”, Ann. Scuola Norm. Sup. Pisa CL. $4^e$ serie, 14:1 (1987), 123–141 | MR | Zbl

[10] N. Hirano,W. S. Kim, “Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity”, Nonlinear Anal., 26:6 (1996), 1143–1160 | DOI | MR | Zbl

[11] W. S. Kim, “Multiple existence of periodic solutions for similinear parabolic equations with large source”, Houston J. Math., 30:1 (2004), 283–295 | MR | Zbl

[12] W. S. Kim, “Existence of multiple periodic solutions for semilinear parabolic equations with sublinear growth nonlinearities”, J. Korean Math. Soc., 46:4 (2009), 691–699 | DOI | MR | Zbl

[13] Yu. G. Borisovich [i dr.], Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, KomKniga, M., 2005, 216 pp. | MR

[14] V. N. Pavlenko, “Uravneniya parabolicheskogo tipa s razryvnoi nelineinostyu stepennogo rosta”, Vest. Chelyab. gos. un. Matematika. Mekhanika. Informatika, 2008, no. 10, 49–53 | Zbl

[15] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967, 624 pp. | MR