The positive equilibrium solution exists of a Holling-IV type predator-prey model with homogeneous Dirichlet boundary condition is concerned in this paper. First,the model is equivalent to an elliptic boundary problem to make a priori estimate of positive solutions. Then,by using the degree theory, calculating the index of the fixed point of the compact map in cone and combining with the operator spectrum analysis,some sufficient conditions for the existence of positive equilibrium solutions are obtained. The result shows that the existence of the positive solution is closely related to the eigenvalues of differential operators derived from the model.%研究了一类在齐次Dirichlet边界条件下的Holling-Ⅳ型捕食-食饵模型正平衡解的存在性.首先,将该模型等价为椭圆边值问题,对正解做出先验估计.然后,利用度理论和锥映射的不动点计算方法,再结合算予谱分析,得出该模型存在正平衡解的充分条件.结果表明,该模型正平衡解的存在性与模型的导算子的特征值密切相关.
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