Periodic Non-Negative Solutions for Anisotropic p(z)-Laplacian Parabolic Equations with Strong Nonlinearity

Abstract

In this paper, we investigate a degenerate parabolic equation involving an anisotropic p(z)-Laplacian operator and a strongly nonlinear source term, subject to Dirichlet-type boundary conditions. Our main objective is to establish the existence of a nonnegative periodic solution. The proof relies on the Leray–Schauder topological degree, whose application in this framework requires a careful treatment due to the degeneracy of the operator and the nonlinear nature of the source.