| Title:
|
Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue (English) |
| Author:
|
Drábek, Pavel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
26 |
| Issue:
|
4 |
| Year:
|
1981 |
| Pages:
|
304-311 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper existence and multiplicity of solutions of the elliptic problem $\Cal L u + \lambda_1u+\mu u^+vu^-+g(x,u)=f$ in $\Omega$ $Bu=0$ on $\partial\Omega$, are discussed provided the parameters $\mu$ and $v$ are close to the first eigenvalue $\lamda_1$. The sufficient conditions presented here are more general than those in given by S. Fučík in his aerlier paper. (English) |
| Keyword:
|
multiplicity of solutions |
| Keyword:
|
weakly nonlinear elliptic equations |
| MSC:
|
35J60 |
| MSC:
|
47J05 |
| MSC:
|
73C50 |
| idZBL:
|
Zbl 0469.35051 |
| idMR:
|
MR0623508 |
| DOI:
|
10.21136/AM.1981.103919 |
| . |
| Date available:
|
2008-05-20T18:17:17Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103919 |
| . |
| Reference:
|
[1] A. Ambrosetti G. Mancini: Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue.Journal of Diff. Eq., vol. 28, (1978), 220-245. MR 0492839, 10.1016/0022-0396(78)90068-2 |
| Reference:
|
[2] S. Fučík: Remarks on a result by A. Ambrosetti and G. Prodi.U.M.I., (4), 11 (1975), 259-267. MR 0382849 |
| Reference:
|
[3] M. A. Krasnoselskij: Topological methods in the theory of nonlinear integral equations.Pergamon Press, London, 1964. |
| Reference:
|
[4] J. Minty: Monotone operators in Hilbert space.Duke Math. Journal 29 (1962), 341 - 346. MR 0169064, 10.1215/S0012-7094-62-02933-2 |
| Reference:
|
[5] A. N. Kolmogorov S. V. Fomin: Элементы теории функций и функционального анализа.Nauka, Moskva, 1972. |
| . |
