Existence of three solutions for a class of quasilinear elliptic systems involving the (p(x), q(x))-Laplacian

We study the solutions of the (p(x),q(x))(p(x),q(x))-Laplacian equations with Dirichlet boundary condition on a bounded domain, and obtain three solutions under appropriate hypotheses. Our technical approach is based on the general three-critical-points theorem obtained by B. Ricceri.