General Quasilinear Problems Involving P(X)-Laplacian with Robin Boundary Condition

Abstract

This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving p(x)-Laplace type equation, namely {−div(a(|∇u|p(x))|∇u|p(x)−2∇u)=λf(x,u)n⋅a(|∇u|p(x))|∇u|p(x)−2∇u+b(x)|u|p(x)−2u=g(x,u)inonΩ,∂Ω. Our technical approach is based on variational methods, especially, the mountain pass theorem and the symmetric mountain pass theorem.