具混合边界条件的捕食模型正稳态解的存在性

Existence of positive steady-state solutions for a predator-prey model with mixed boundary conditions

文章利用拓扑度理论、指数理论和比较原理,结合逼近方法和一定的数学分析技巧,通过分析构造的一个Frechet可微的紧算子,对建立的一类带有混合边界条件的具有扩散和比例依赖响应函数的捕食模型进行研究,证明了该算子在一定条件下至少存在一个正的不动点,获得了捕食模型解的渐近性态,同时证明该模型至少存在一个正稳态解。

A ratio-dependent functional response predator-prey model with mixed boundary conditions and diffusion is established. By using the topologic degree theory, index theory, comparison princi- ple,the approximation methods and some mathematical analysis skills and by constructing a compact Frechet differentiable operator,it is proved that under some conditions the operator possesses at least a positive fixed point. The asymptotic state is obtained,and it is also proved that the model possesses at least a positive steady-state solution.