Ground state solutions for a class of elliptic Dirichlet problems involving the p(x)-Laplacian

被引：4

作者：

Ge, Bin ^{[1
]}

Zhuge, Xiang-Wu ^{[1
]}

Yuan, Wen-Shuo ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2021年 / 11卷 / 03期

基金：

中国国家自然科学基金;

关键词：

p(x)-Laplacian equation; Variable exponent Sobolev space; Ground state solutions; Multiple solutions; Nehari manifold; 35J60; 35J70; 35D30; VARIABLE EXPONENT; EXISTENCE; MULTIPLICITY; FUNCTIONALS; PRINCIPLE; EQUATIONS;

D O I：

10.1007/s13324-021-00562-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in the existence and multiplicity of ground state solutions for a class of p(x)-Laplacian Dirichlet problem in bounded domains. Firstly, combining constraint variational method and quantitative deformation lemma, we prove that the equation possesses at least one least energy sign-changing solution with exactly two nodal domains. Finally, using a strong maximum principle, we obtain three ground state solutions (one positive, one negative, and one sign-changing) for this problem.

引用

页数：25

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