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November/December 2011 Indefinite quasilinear elliptic equations in exterior domains with exponential critical growth
Claudianor O. Alves, Sérgio H M. Soares, Luciana Rôze de Freitas
Differential Integral Equations 24(11/12): 1047-1062 (November/December 2011). DOI: 10.57262/die/1356012875

Abstract

This paper is concerned with the existence of solutions for the quasilinear problem \[ \left \{ \begin{array}{lll} -div( \left|\nabla u\right| ^{N-2}\nabla u ) + \left| u\right|^{N-2}u= a(x)g(u)\quad \mbox{in}\ \Omega\\ \quad u=0\quad \mbox{on}\ \partial\Omega , \end{array} \right. \] where $\Omega \subset \mathbb{R}^N$ ($N\geq 2$) is an exterior domain; that is, $\Omega = \mathbb{R}^{N} \setminus \omega $, where $w \subset \mathbb{R}^{N}$ is a bounded domain, the nonlinearity $g(u)$ has an exponential critical growth at infinity and $a(x)$ is a continuous function and changes sign in $\Omega$. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

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Claudianor O. Alves. Sérgio H M. Soares. Luciana Rôze de Freitas. "Indefinite quasilinear elliptic equations in exterior domains with exponential critical growth." Differential Integral Equations 24 (11/12) 1047 - 1062, November/December 2011. https://doi.org/10.57262/die/1356012875

Information

Published: November/December 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35085
MathSciNet: MR2866010
Digital Object Identifier: 10.57262/die/1356012875

Subjects:
Primary: 35J35 , 35J60 , 35J65

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 11/12 • November/December 2011
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