Stationary Patterns for a Lotka-Volterra Cooperative Model with a Density-Dependent Diffusion Term

Abstract

This paper is concerned with positive stationary solutions for a Lotka-Volterra cooperative model with a density-dependent diffusion term of a fractional type. The existence of stationary patterns is proven by the presence of density-dependent diffusion. Our proof is based on the Leray-Schauder degree theory and some a priori estimates. We also derive a certain limiting system which positive stationary solutions satisfy.