一类带有交叉扩散的捕食-食饵模型的正解

Abstract

Abstract:

A predator-prey model with cross diffusion under homogeneous Dirichlet boundary conditions is investigated. Firstly, the existence of positive solutions can be established by the Leray-Schauder degree theory. Secondly, we consider that the existence of positive solutions of the regular perturbation system and the singular perturbation system when m=β is sufficiently large, respectively, and moreover, we show that the positive solutions of the singular perturbation system will blow up along the continuum at a^* by the bifurcation theory. Finally, the multiplicity results of positive solutions of system is also considered.

Key words: Cross diffusion, Bifurcation, Positive solutions

CLC Number:

O175.26

Hailong Yuan,Yuping Wang,Yanling Li. Positive Solutions of a Predator-Prey Model with Cross Diffusion[J].Acta mathematica scientia,Series A, 2019, 39(3): 545-559.

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References 25

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Positive Solutions of a Predator-Prey Model with Cross Diffusion

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