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

Abstract

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.