Document Type

Article

Publication Date

10-2016

Keywords

general elliptic system, positive solution

Abstract

The purpose of this paper is to give a sufficient condition for the existence and nonexistence of positive solutions to a rather general type of elliptic system of the Dirichlet problem on the bounded domain Ω in Rn. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are upper-lower solutions, eigenvalues of operators, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

Journal Title

International Electronic Journal of Pure and Applied Mathematics

Volume

10

Issue

2

First Page

115

Last Page

125

DOI

https://doi.org/10.12732/iejpam.v10i2.2

First Department

Mathematics

Acknowledgements

Retrieved March 29, 2018, from http://www.e.ijpam.eu/contents/articles/201601002002.pdf

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