Nonnegative solutions for a heterogeneous degenerate competition model

Abstract

This paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as uniqueness of positive solution. In order to obtain the results we employ monotonicity methods, singular spectral theory and a fixed point index.