Existence of the Positive Solutions of a Kind of Reaction-Diffusion System
Wang Lizhou，Huang Aixiang
(School of Sciences, Xi'an Jiaotong University, Xi'an 710049，China)

Abstract: Using the method of upper and lower solutions principle, the coexistence steady-states of a kind of reaction-diffusion system in ecology, the Volterra-Lotka model is studied. The bifurcation structure of the positive solutions is discussed for the cooperating model in the case of equal birth rates. Some existence, nonexistence and uniqueness results are presented. The results show that understanding of this kind of reaction-diffusion system depends seriously on our knowledge about the single semilinear elliptic equations.
Keywords: upper and lower solutions principle;reaction-diffusion system;positive solution