Advances in Differential Equations

On a variational problem involving critical Sobolev growth in dimension four

Mokhless Hammami and Mohamed ben Ayed

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867950

Mathematical Reviews number (MathSciNet)
MR2100634

Zentralblatt MATH identifier
1216.35030

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35B33: Critical exponents 35J60: Nonlinear elliptic equations 47J30: Variational methods [See also 58Exx] 49J10: Free problems in two or more independent variables 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

ben Ayed, Mohamed; Hammami, Mokhless. On a variational problem involving critical Sobolev growth in dimension four. Adv. Differential Equations 9 (2004), no. 3-4, 415--446. https://projecteuclid.org/euclid.ade/1355867950.


Export citation