MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

被引：0

作者：

尚月赟 ^{[1
,2
]}

王莉 ^{[3
]}

机构：

[1] Department of Mathematics, Huazhong Normal University

[2] Department of Mathematics, South-Central University for Nationalities

[3] School of Basic Science, East China Jiaotong University

来源：

ActaMathematicaScientia | 2014年 / 34卷 / 05期

关键词：

nontrivial solutions; polyharmonic problems; critical exponents; variational methods;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the following problem:(-△)ku = λf(x)|u|q-2u + g(x)|u|k*-2u, x ∈Ω,u ∈ Hk0(Ω),where Ω is a bounded domain in RNwith N ≥ 2k + 1, 1 < q < 2, λ > 0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k* =2N N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.

引用

页码：1495 / 1509

页数：15

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