Year: 2023
Author: Timothy Robertson, Joon Hyuk Kang, Timothy Robertson
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 122–146
Abstract
The purpose of this paper is to give a sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain $Ω$ in $R^n.$ Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n2.2
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 122–146
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Competition system coexistence state.