Existence of positive solutions of Lotka-Volterra competition model with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Existence of positive solutions of Lotka-Volterra competition model with nonlinear boundary conditions
zbMATH Open document ID: 1470.35160
DOI: 10.1155/2014/102180
author: Yang Zhang
author: Mingxin Wang
author: Yuwen Wang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that \(- d_1 \Delta u = u(a_1 - b_1 u - c_1 v)\), \(x \in \Omega\); \(- d_2 \Delta v = v(a_2 - b_2 u - c_2 v)\), \(x \in \Omega\); \(\partial u / \partial \nu + f(u) = 0\), \(x \in \partial \Omega\); \(\partial v / \partial \nu + g(v) = 0\), \(x \in \partial \Omega\), has no positive solution when one of the diffusion coefficients is sufficiently large.
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 7021735
Wikidata QID: Q59035198
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/102180
OpenAlex ID: W2053157769
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description: scientific article; zbMATH DE number 7021735