A Lotka–Volterra symbiotic model with cross-diffusion

The main goal of this paper is to study the existence and non-existence of coexistence states for a Lotka–Volterra symbiotic model with cross-diffusion. We use mainly bifurcation methods and a priori bounds to give sufficient conditions in terms of the data of the problem for the existence of positive solutions. We also analyze the profiles of the positive solutions when the cross-diffusion parameter goes to infinity.