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

摘要

The aim of this paper is to investigate a class of nonlinear periodic systems involving general differential operators with variable exponents. We assume that the reactions contain strong nonlinearities with p(x)-growth conditions on the gradients of the solutions. By using Leray Schauder’s topological degree combined with the sub- and super-solutions method, we prove the existence of weak periodic solutions to the considered systems.