## Differential and Integral Equations

### Existence results for a nonlinear elliptic equation with critical Sobolev exponent

#### 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