Infinitely many non-negative solutions for a Dirichlet problem involving p(x)p(x)-Laplacian

In this paper, we consider a Dirichlet problem involving the p(x)p(x)-Laplacian of the type View the MathML source{−div(|∇u|p(x)−2∇u)=f(x,u)in Ω,u=0on ∂Ω. Turn MathJax on We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces