带混合边界条件的Holling-Ⅱ型捕食模型正稳态解的存在性  

Existence of positive stationary solutions for a prey-predator model with Holling-Ⅱ type interactions and the mixed boundary conditions

作　　者：张云[1] 曾宪忠[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《纯粹数学与应用数学》2011年第4期523-532,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(10971061);湖南省自然科学基金(09JJ6013)

摘　　要：研究了一个带混合边界条件的Holling-Ⅱ型捕食模型.通过构造一个微分紧算子K,借助锥内不动点指数理论、拓扑度理论、椭圆方程估计理论和极值原理证得了算子K存在正的不动点,此结论表明捕食模型存在正解,即物种共存状态.This paper investigates a prey-predator model with Holling-Ⅱ type interactions and mixed boundary conditions. By constructing a compact and Frechet differentiable operator , and by using the theory of the fixed point index in cones, the estimates theory of the elliptic equations, the degree theory and the Maximum principle, we obtain under some conditions which possesses at least a positive fixed point, which implies that the prey-predator model possesses at least a positive steady-state solution, namely, co-existence states of two species.

关 键 词：Holling-Ⅱ型捕食模型 正稳态解的存在性 不动点 指数理论 度理论 

分 类 号：O175.25[理学—数学]