Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems

Advances in Mathematical Physics

Haibo Chen¹  Senli Liu¹  Jie Yang² 

[1] School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China, csu.edu.cn;School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China, csu.edu.cn;Department of Mathematics, Huaihua University, Huaihua, Hunan 418008, China, hhtc.edu.cn;

DOI  :  10.1155/2020/8237492

来源: publisher

【 摘 要 】

We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory.

【 授权许可】

Unknown