Periodic solutions of p-Laplacian systems with a nonlinear convection term

Abstract

In this work, we study the existence of periodic solutions for the evolution of p-Laplacian system and we show that these periodic solutions belong to $L^{\infty}(\omega, W^{1,\infty}(\Omega))$ and give a bound of $\left \Vert \nabla u_{i}(t)\right \Vert_{\infty}$ under certain geometric conditions on $\partial \Omega$.