Differential and Integral Equations

Existence results for a nonlinear elliptic equation with critical Sobolev exponent

Mohamed Ben Ayed and Hichem Chtioui

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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.

Article information

Source
Differential Integral Equations, Volume 18, Number 1 (2005), 1-18.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060233

Mathematical Reviews number (MathSciNet)
MR2105336

Zentralblatt MATH identifier
1212.35145

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 47J30: Variational methods [See also 58Exx]

Citation

Ben Ayed, Mohamed; Chtioui, Hichem. Existence results for a nonlinear elliptic equation with critical Sobolev exponent. Differential Integral Equations 18 (2005), no. 1, 1--18. https://projecteuclid.org/euclid.die/1356060233


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