Coexistence of Two Species in a Strongly Coupled Schoener's Competitive Model

This paper deals with the existence of positive solution to a strongly coupled system with homogeneous Dirichlet boundary conditions describing a Schoener's competitive interaction of two species. Making use of the Schauder fixed point theorem, a sufficient condition is given for the system to have a coexistence. And true solutions are constructed based on monotone iterative method. Our results show that this model possesses at least one coexistence state if cross-diffusions and intra-specific competitions are weak.