### On a variational problem involving critical Sobolev growth in dimension four

#### Abstract

In this paper we consider the following nonlinear elliptic problem: $-\Delta u=Ku^3,$ $u>0$ in $\Omega$, $u=0$ on $\partial\Omega$, where $K$ is a positive function and $\Omega$ is a bounded domain of $R^4$. We prove a version of the Morse lemma at infinity for this problem, which allows us to describe the critical points at infinity of the associated variational problem. Using a topological argument, we are able to prove an existence result.

#### Article information

Source
Adv. Differential Equations Volume 9, Number 3-4 (2004), 415-446.

Dates
First available in Project Euclid: 18 December 2012