Abstract
This paper is concerned with a modified Leslie-Gower predator-prey model with general functional response under homogeneous Robin boundary conditions. We establish the existence of coexistence states by the fixed index theory on positive cones. As an example, we apply the obtained results to this model with Holling-type II functional response. Our results show that the intrinsic growth rates and the principle eigenvalues of the corresponding elliptic problems with respect to the Robin boundary conditions play more important roles than other parameters for the existence of positive solutions.MSC: 35J55, 37B25, 92D25.
Highlights
1 Introduction Population ecology is dominated by a focus on interspecific interaction such as competition, cooperation and predation in recent research papers
Predator-prey systems are very important to describe the interactions in the multi-species population dynamics
Motivated by the previous works, in this paper, we introduce diffusion into system ( . ) and consider the following partial differential equations equipped with homogeneous Robin boundary conditions:
Summary
Population ecology is dominated by a focus on interspecific interaction such as competition, cooperation and predation in recent research papers. We shall establish the existence of positive solutions to the following elliptic system: In Section , we collect some known results including the eigenvalue problem and the fixed point index on positive cones.
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