Periodic non-negative solutions for anisotropic p(z)-Laplacian parabolic equations with strong nonlinearity

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.