带混合边界条件的Holling-Ⅱ型捕食模型正稳态解的存在性

摘要

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 o%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．