Coexistence in a strongly coupled system describing a two-species cooperative model

This paper is concerned with a cooperative two-species Lotka–Volterra model. Using the fixed point theorem, the existence results of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions are obtained. Our results show that this model possesses at least one coexistence state if the birth rates are big and cross-diffusions are suitably weak.