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2003 Some multiplicity results for a superlinear elliptic problem in $\mathbb R^N$
Addolorata Salvatore
Topol. Methods Nonlinear Anal. 21(1): 29-39 (2003).

Abstract

In this paper we shall study the semilinear elliptic problem $$ \begin{cases} -\Delta u +\sigma(x)u= |u|^{p-2}u + f(x) & \text{in }\mathbb R^N,\\ u\rightarrow 0\quad\text{as } |x| \rightarrow\infty, \end{cases} $$ where $\sigma(x) \rightarrow\infty$ as $| x| \rightarrow\infty$, $p> 2$ and $f\in L^{2}(\mathbb R^{N})$. Thanks to a compact embedding of a suitable weigthed Sobolev space in $L^{2}(\mathbb R^{N})$, a direct use of the Symmetric Mountain Pass Theorem (if $f=0$) and of the fibering method (if $f\neq 0$) allows to extend some multiplicity results, already known in the case of bounded domains.

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Addolorata Salvatore. "Some multiplicity results for a superlinear elliptic problem in $\mathbb R^N$." Topol. Methods Nonlinear Anal. 21 (1) 29 - 39, 2003.

Information

Published: 2003
First available in Project Euclid: 30 September 2016

zbMATH: 1046.35110
MathSciNet: MR1980134

Rights: Copyright © 2003 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.21 • No. 1 • 2003
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