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2004 On a variational problem involving critical Sobolev growth in dimension four
Mokhless Hammami, Mohamed ben Ayed
Adv. Differential Equations 9(3-4): 415-446 (2004).

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.

Citation

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Mokhless Hammami. Mohamed ben Ayed. "On a variational problem involving critical Sobolev growth in dimension four." Adv. Differential Equations 9 (3-4) 415 - 446, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1216.35030
MathSciNet: MR2100634

Subjects:
Primary: 35J20
Secondary: 35B33, 35J60, 47J30, 49J10, 58E05

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 3-4 • 2004
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