毒素影响下的捕食-食饵模型正解的存在性

Existence of positive solutions for the predator-prey model with toxicity

研究了一类带Monod-Haldane反应项的捕食-食饵模型在齐次Dirichlet边界条件下的平衡态问题.首先通过极值原理和上下解方法给出了正解的先验估计;其次利用Leray-Schauder度理论得到了正解存在的充分条件;最后运用线性化算子及Riesz-Schauder理论说明了平衡态问题的平凡解和半平凡解的局部渐近稳定性.

The steady-state of the predator-prey model with Monod-Haldane functional response under homogenous Dirichet boundary conditions is studied.Firstly,the prior estimate of positive solutions is given by the principle of extreme value and the upper and lower solution method.Secondly,by using the leray-Schauder degree theory,sufficient conditions for the existence of positive solutions are obtained.Finally,according to the linear operator and Riesz-Schauder theory,the local asymptotic stability of the trivial solution and the semi-trivial solutions of the equilibrium state problem are illustrated.