Positive steady states for a nonlinear diffusion Beddington-DeAngelis model

Abstract

The main purpose of this work is to investigate the effects of nonlinear diffusion on positive steady states in a Beddington-DeAngelis model. By the energy method and Leray-Schauder degree theory, we consider the non-existence and existence of concerning non-constant positive steady states of the model. We demonstrate that nonlinear diffusion can create non-constant positive steady-state solutions even when the random diffusion fails to do so.