Geodesic
The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (1998), pp. 69-76.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{IVM_1998_11_a9,
     author = {V. N. Pavlenko and O. V. Ul'yanova},
     title = {The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {69--76},
     publisher = {mathdoc},
     number = {11},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_1998_11_a9/}
}
TY  - JOUR
AU  - V. N. Pavlenko
AU  - O. V. Ul'yanova
TI  - The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 1998
SP  - 69
EP  - 76
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_1998_11_a9/
LA  - ru
ID  - IVM_1998_11_a9
ER  - 
%0 Journal Article
%A V. N. Pavlenko
%A O. V. Ul'yanova
%T The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 1998
%P 69-76
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_1998_11_a9/
%G ru
%F IVM_1998_11_a9
V. N. Pavlenko; O. V. Ul'yanova. The method of upper and lower solutions for elliptic-type equations with discontinuous nonlinearities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (1998), pp. 69-76. http://geodesic.mathdoc.fr/item/IVM_1998_11_a9/

[1] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964, 540 pp. | MR

[2] Pavlenko V. N., “O suschestvovanii polupravilnykh reshenii pervoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s razryvnoi nemonotonnoi nelineinostyu”, Differents. uravneniya, 27:3 (1991), 520–526 | MR | Zbl

[3] Amann H., “On the number of solutions of nonlinear equations in ordered Banach spaces”, J. Funct. Anal., 11:3 (1972), 346–384 | DOI | MR | Zbl

[4] Amann H., “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces”, SIAM Review, 18:4 (1976), 620–709 | DOI | MR | Zbl

[5] Amann H., “Supersolutions, monotone iterations, and stability”, J. Different. Equat., 21:2 (1976), 363–377 | DOI | MR | Zbl

[6] Amann H., “Existence and multiplicity theorems for semi-linear elliptic boundary value problems”, Math. Z., 150:3 (1976), 281–295 | DOI | MR | Zbl

[7] Amann H., Crandall M. G., “On some existence theorems for semi-linear elliptic equations”, Indiana Univ. Math. J., 27:5 (1978), 779–790 | DOI | MR | Zbl

[8] Stuart C. A., “Maximal and minimal solutions of elliptic differential equations with discontinuous nonlinearities”, Math. Z., 163:3 (1978), 239–249 | DOI | MR | Zbl

[9] Stuart C. A., Toland J. F., “A property of solutions of elliptic differential equations with discontinuous nonlinearities”, J. London Math. Soc., Ser. 2, 21:2 (1980), 329–335 | DOI | MR | Zbl

[10] Basile N., Mininni M., “Some solvability results for elliptic boundary value problems in resonance at the first eigenvalue with discontinuous nonlinearities”, Boll. Unione Mat. Ital. Ser. 5, B-17:3 (1980), 1023–1033 | MR | Zbl

[11] Massabo I., “Elliptic boundary value problems at resonance with discontinuous nonlinearities”, Boll. Unione Mat. Ital. Ser. 5, B-17:3 (1980), 1308–1320 | MR | Zbl

[12] Carl S., “The monotone iterative technique for a parabolic boundary value problems with discontinuous nonlinearity”, Nonlinear Anal., 13:12 (1989), 1399–1407 | DOI | MR | Zbl

[13] Carl S., Heikkila S., “On a parabolic boundary value problems with discontinuous nonlinearity”, Nonlinear Anal., 15:11 (1990), 1091–1095 | DOI | MR | Zbl

[14] Pavlenko V. N., “Suschestvovanie silnykh reshenii uravnenii parabolicheskogo tipa s razryvnymi nelineinostyami”, UMN, 50:4 (1995), 127–128

[15] Chang K. C., “The obstacle problem and partial differential equations with discontinuous nonlinearities”, Comm. Pure Appl. Math., 33:2 (1980), 117–146 | DOI | MR | Zbl

[16] Pavlenko V. N., “Variatsionnyi metod dlya uravnenii s razryvnymi operatorami”, Vestn. Chelyabinsk. un-ta. Ser. matem., mekhan., 1994, no. 1, 87–85 | MR

[17] Pavlenko V. N., “Variatsionnyi metod dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, UMN, 49:4 (1994), 138

[18] Agmon S., Duglis A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, In. lit., M., 1962, 208 pp. | Zbl

[19] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962, 396 pp. | MR

[20] Pavlenko V. N., “Metod monotonnykh operatorov v zadachakh upravleniya raspredelennymi sistemami ellipticheskogo tipa s razryvnymi nelineinostyami”, Izv. vuzov. Matematika, 1993, no. 8, 49–54 | MR | Zbl

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

[22] Browder F. E., “Nonlinear maximal monotone operators in Banach space”, Math. Ann., 175:2 (1968), 89–113 | DOI | MR | Zbl

[23] Gilbarg D., Trudinger M., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR | Zbl