Infinitely many non-negative solutions for a p(x)p(x)-Kirchhoff-type problem with Dirichlet boundary condition

In this paper, we consider the Dirichlet problem involving the p(x)p(x)-Kirchhoff-type {−(a+b∫Ω1p(x)|∇u|p(x)dx)div(|∇u|p(x)−2∇u)=f(x,u)inΩ,u=0on∂Ω. 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.