具有Beddington-DeAngelis功能反应函数捕食模型正稳态解存在性

The Existence of Positive Steady-state Solutions for a Beddington-DeAngelis Functional Response Predator-prey Model

利用反应扩散方程研究具有响应函数的种群动力学捕食模型已成为非线性偏微分方程领域中的一个非常重要的研究方向.利用拓扑度理论、指数理论、椭圆方程估计理论和极值原理研究了一类带有混合边界条件的Beddington-DeAngelis功能反应函数的捕食模型.结合一定的数学分析技巧,获得了捕食模型解的渐近性态和至少存在一个正稳态解的条件.鉴于种群的长时行为与捕食反应扩散系统相应的平衡态问题密切相关,因此研究捕食反应扩散系统正平衡态解的存在性有着十分重要的理论和现实意义.

The population dynamics predator-prey models with functional response have received intensive research by using reaction-diffusion equations which is an important aspect in the field of nonlinear partial differential equations.By using the topological degree theory,the index theory,the estimation theory of elliptic equations and the Maximum principle,and associating some mathematical analysis techniques,a Beddington-DeAngelis functional response predator-prey model is investigated with the third boundary conditions of mixed boundary conditions.The asymptotic behavior and the existance of at least one positive steady-state solution of the model are obtained.In view of the long time behavior of a population being closely related to the corresponding equilibrium problem of predator-prey reaction-diffusion systems,the existence of positive equilibrium solution of the predator-prey reaction diffusion system has very important theoretical and practical significance.