Existence of the positive steady states of a reaction–diffusion–advection competition model

Abstract

In this paper, we investigate a reaction–diffusion–advection two-species competition biological model by employing the methods of Lyapunov–Schmidt reduction, perturbation theory and the implicit function theorem and so on. For any given diffusion rates we obtain the existence of positive steady states by using the advection rate η and the competitive coefficients c and b as the bifurcation parameters.