Mountain pass solution for the weighted Dirichlet (p(z), q(z))-problem

We consider the Dirichlet boundary value problem for equations involving the (p(z), q(z))-Laplacian operator in the principal part on an open bounded domain Omega subset of R-n. Here, the p(z)-Laplacian is weighted by a function a is an element of L-infinity(Omega)(+), and the nonlinearity in the reaction term is allowed to depend on the solution without imposing the Ambrosetti-Rabinowitz condition. The proof of the existence of solution to our problem is based on a mountain pass critical point approach with the Cerami condition at level c.