ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

被引：167

作者：

Alves, C. O. ^{[1
]}

Correa, F. J. S. A. ^{[1
]}

Figueiredo, G. M. ^{[2
]}

机构：

[1] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58109970 Campina Grande, PB, Brazil

[2] Univ Fed Para, Fac Matemat, BR-66075110 Belem, Para, Brazil

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2010年 / 2卷 / 03期

关键词：

variational methods; nonlocal problems; Kirchhoff equation; critical growth;

D O I：

10.7153/dea-02-25

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type -[M(integral(Omega)|del u|(2) dx)] Delta u = lambda f(x,u)+u(5) in Omega, u(x) > 0 in Omega and u = 0 on partial derivative Omega, where Omega subset of R-N, for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and lambda is a positive parameter. Our approach is based on the variational method.

引用

页码：409 / 417

页数：9