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2005 Existence results for a nonlinear elliptic equation with critical Sobolev exponent
Mohamed Ben Ayed, Hichem Chtioui
Differential Integral Equations 18(1): 1-18 (2005).

Abstract

In this paper we study the following nonlinear elliptic problem with Dirichlet boundary condition: $-\Delta u =K(x)u^p$, $u>0$ in $\Omega$, $u =0$ on $ \partial \Omega$, where $\Omega$ is a bounded, smooth domain of $\mathbb R^n$, $n\geq 4$ and $p+1=2n/(n-2)$ is the critical Sobolev exponent. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational problem, we prove some existence results.

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Mohamed Ben Ayed. Hichem Chtioui. "Existence results for a nonlinear elliptic equation with critical Sobolev exponent." Differential Integral Equations 18 (1) 1 - 18, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35145
MathSciNet: MR2105336

Subjects:
Primary: 35J60
Secondary: 35B33 , 47J30

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 1 • 2005
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