THREE NONTRIVIAL SOLUTIONS FOR NONCOERCIVE ASYMPTOTICALLY LINEAR ELLIPTIC PROBLEMS

被引：0

作者：

Hu, Shouchuan ^{[1
,3
]}

Papageorgiou, N. S. ^{[2
]}

机构：

[1] Shandong Normal Univ, Coll Math, Jinan, Shandong, Peoples R China

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[3] Missouri State Univ, Dept Math, Springfield, MO 65804 USA

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2011年 / 37卷 / 02期

关键词：

PS-condition; local minimizer; critical point of mountain pass-type; critical groups; Poincare-Hopf formula; three nontrivial solutions; regularity; CRITICAL-POINT; EQUATIONS; H-1;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider a semilinear elliptic equation. We assume that the right and side nonlinearity is asymptotically linear and our conditions on it imply that the Euler functional of the problem is noncoercive. Using variational methods coupled with Morse theory and in particular the use of critical groups, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign.

引用

页码：559 / 576

页数：18

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