A reaction-diffusion system of a competitor-competitor-mutualist model
We investigate the homogeneous Dirichlet problem and Neumann problem to a reaction-diffusion system of a competitor-competitor-mutualist model. The existence, uniqueness, and boundedness of the solutions are established by means of the comparison principle and the monotonicity method. For the Dirichlet problem, we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities. For the Neumann problem, we analyze the constant equilibrium solutions and their stabilities. The main method used in studying of the stabilities is the spectral analysis to the linearized operators. The O.D.E. problem to the same model was proposed and studied by \textit{B. Rai}, \textit{H. I. Freedman}, and \textit{J. F. Addicott} [Math. Biosci. 65, 13-50 (1983; Zbl 0532.92025)].
scientific article; zbMATH DE number 4075652