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

被引：0
|
作者：
Bin Ge
Xiang-Wu Zhuge
Wen-Shuo Yuan
机构：
[1] Harbin Engineering University,College of Mathematical Sciences
来源：
Analysis and Mathematical Physics | 2021年 / 11卷
关键词：
(; )-Laplacian equation; Variable exponent Sobolev space; Ground state solutions; Multiple solutions; Nehari manifold; 35J60; 35J70; 35D30;
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学科分类号：
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.
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