Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator

We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the p(x)-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.