Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue

Pavel Drábek

Aplikace matematiky (1981)

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

Abstract

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In this paper existence and multiplicity of solutions of the elliptic problem u + λ 1 u + μ u + v u - + g ( x , u ) = f in Ω B u = 0 on Ω , are discussed provided the parameters μ 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.

How to cite

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Drábek, 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

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  1. A. Ambrosetti G. Mancini, 10.1016/0022-0396(78)90068-2, Journal of Diff. Eq., vol. 28, (1978), 220-245. (1978) Zbl0393.35032MR0492839DOI10.1016/0022-0396(78)90068-2
  2. S. Fučík, Remarks on a result by A. Ambrosetti and G. Prodi, U.M.I., (4), 11 (1975), 259-267. (1975) MR0382849
  3. M. A. Krasnoselskij, Topological methods in the theory of nonlinear integral equations, Pergamon Press, London, 1964. (1964) 
  4. J. Minty, 10.1215/S0012-7094-62-02933-2, Duke Math. Journal 29 (1962), 341 - 346. (1962) Zbl0111.31202MR0169064DOI10.1215/S0012-7094-62-02933-2
  5. A. N. Kolmogorov S. V. Fomin, Элементы теории функций и функционального анализа, Nauka, Moskva, 1972. (1972) 

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