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

Abstract We study the solutions of the ( 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.