Positive periodic solutions for a system of anisotropic parabolic equations

Abstract

We consider a system of two degenerate parabolic equations with nonlocal terms and Dirichlet boundary conditions. More precisely, the degeneracy in each equation of the system is of the type r ( x ) -Laplacian where r ( x ) is a function depending on x ∈ Ω , where Ω is a bounded smooth domain of R n . The system models the diffusion and the interaction between two different biological species sharing the same territory Ω. The paper provides conditions on the parameters of the problem that guarantee the coexistence of a T-periodic non-negative solution ( u , v ) with both non-trivial u , v .