# Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue

Aplikace matematiky (1981)

- Volume: 26, Issue: 4, page 304-311
- ISSN: 0862-7940

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topDrábek, Pavel. "Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue." Aplikace matematiky 26.4 (1981): 304-311. <http://eudml.org/doc/15202>.

@article{Drábek1981,

abstract = {In this paper existence and multiplicity of solutions of the elliptic problem $\mathcal \{L\} u + \lambda _1u+\mu u^+vu^-+g(x,u)=f$ in $\Omega $$Bu=0$ on $\partial \Omega $, are discussed provided the parameters $\mu $ and $v$ are close to the first eigenvalue $_1$. The sufficient conditions presented here are more general than those in given by S. Fučík in his aerlier paper.},

author = {Drábek, Pavel},

journal = {Aplikace matematiky},

keywords = {multiplicity of solutions; weakly nonlinear elliptic equations; multiplicity of solutions; weakly nonlinear elliptic equations},

language = {eng},

number = {4},

pages = {304-311},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue},

url = {http://eudml.org/doc/15202},

volume = {26},

year = {1981},

}

TY - JOUR

AU - Drábek, Pavel

TI - Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue

JO - Aplikace matematiky

PY - 1981

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 26

IS - 4

SP - 304

EP - 311

AB - In this paper existence and multiplicity of solutions of the elliptic problem $\mathcal {L} u + \lambda _1u+\mu u^+vu^-+g(x,u)=f$ in $\Omega $$Bu=0$ on $\partial \Omega $, are discussed provided the parameters $\mu $ and $v$ are close to the first eigenvalue $_1$. The sufficient conditions presented here are more general than those in given by S. Fučík in his aerlier paper.

LA - eng

KW - multiplicity of solutions; weakly nonlinear elliptic equations; multiplicity of solutions; weakly nonlinear elliptic equations

UR - http://eudml.org/doc/15202

ER -

## References

top- A. Ambrosetti G. Mancini, 10.1016/0022-0396(78)90068-2, Journal of Diff. Eq., vol. 28, (1978), 220-245. (1978) MR0492839DOI10.1016/0022-0396(78)90068-2
- S. Fučík, Remarks on a result by A. Ambrosetti and G. Prodi, U.M.I., (4), 11 (1975), 259-267. (1975) MR0382849
- M. A. Krasnoselskij, Topological methods in the theory of nonlinear integral equations, Pergamon Press, London, 1964. (1964)
- J. Minty, 10.1215/S0012-7094-62-02933-2, Duke Math. Journal 29 (1962), 341 - 346. (1962) MR0169064DOI10.1215/S0012-7094-62-02933-2
- A. N. Kolmogorov S. V. Fomin, Элементы теории функций и функционального анализа, Nauka, Moskva, 1972. (1972)

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