Uniqueness and multiplicity of a prey-predator model with predator saturation and competition
type: Item
instance of: scholarly article
title: Uniqueness and multiplicity of a prey-predator model with predator saturation and competition
zbMATH Open document ID: 1263.92045
DOI: 10.1155/2012/627419
author: Lifeng Li
author: Xiaozhou Feng
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: We investigate the positive solutions of a prey-predator model with predator saturation and competition under homogeneous Dirichlet boundary conditions. First, the existence of positive solutions and some sufficient and necessary conditions are established by using the standard fixed point index theory in cones. Second, the changes of solution branches, multiplicity, uniqueness, and stability of positive solutions are obtained by virtue of bifurcation theory, perturbation theory of eigenvalues, and the fixed point index theory. Finally, the exact number and type of positive solutions are proved when \(k\) or \(m\) converges to infinity.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6169949
Wikidata QID: Q58906268
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/627419
OpenAlex ID: W2022548767
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description: scientific article; zbMATH DE number 6169949