Time periodic solutions for strongly nonlinear parabolic systems with p(x)-growth conditions

Abstract

We study a class of nonlinear periodic systems driven by general differential operators with variable exponent. We assume that the reactions contains p(x)-growth nonlinearities with respect to the gradients. By using Leray Schauder’s topological degree combined with the sub- and super-solutions method, we establish the existence and uniqueness results of weak periodic solutions to the studied systems.