On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent

被引：51

作者：

Ebobisse, F

Ahmedou, MO

机构：

[1] Univ Bonn, Inst Math, D-53115 Bonn, Germany

[2] SISSA, I-34014 Trieste, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 52卷 / 05期

关键词：

critical point at infinity; critical Sobolev exponent; elliptic PDE; lack of compactness; topological methods;

D O I：

10.1016/S0362-546X(02)00273-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we use an algebraic topological argument due to Bahri and Coron to show how the topology of the domain influences the existence of positive solutions of the following problem involving the bilaplacian operator with the critical Sobolev exponent Delta(2)u = u(n+4)/((n-4)) in Omega, u > 0 in Omega, u = Deltau = 0 on partial derivativeOmega, where Q is a bounded domain of R-n (n greater than or equal to 5) with a smooth boundary partial derivativeOmega. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：1535 / 1552

页数：18

共 25 条

[1] ON A VARIATIONAL PROBLEM WITH LACK OF COMPACTNESS - THE TOPOLOGICAL EFFECT OF THE CRITICAL-POINTS AT INFINITY [J].