Existence of solution for a degenerate p(x)-Laplacian equation in RN

Using variational methods we establish the existence of nontrivial solutions for the following class of problems −div a(x)|∇u|p(x)−2∇u + |u|p(x)−2u = K(x)|u|q(x)−2u in RN , where p, q,a, K :RN →R are continuous functions satisfying some conditions and the set {x ∈ RN ; a(x) = 0} is not empty.