Existence and multiplicity of solutions for Dirichlet problem of p(x)-Laplacian type without the Ambrosetti-Rabinowitz condition

This paper deals with the following variational problem with variable exponents{−div((1+|∇u|p(x)1+|∇u|2p(x))|∇u|p(x)−2∇u)=f(x,u),inΩ,u=0,on∂Ω, where Ω⊆RN (N≥2) be a bounded domain with the smooth boundary ∂Ω, p:Ω‾→R is a Lipschitz continuous function with 1更多