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A GENERAL ELLIPTIC NONLINEAR SYSTEM OF MULTIPLE FUNCTIONS WITH APPLICATION

TitleA GENERAL ELLIPTIC NONLINEAR SYSTEM OF MULTIPLE FUNCTIONS WITH APPLICATION
Publication TypeJournal Article
Year of Publication2016
AuthorsRobertson, T, Kang, JHyuk
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume10
Issue2
Start Page139
Pagination12
Date Published11/2016
Type of Articlescientific: mathematics
ISSN1314-0744
Keywordsgeneral elliptic system, positive solution
Abstract
The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rn . We also investigate the effects of perturbation on the positive solutions to the system. The techniques used in this paper are upper-lower solutions, eigenvalues of operators, the maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.
URLhttp://www.e.ijpam.eu/contents/articles/201601002004.pdf
DOI10.12732/iejpam.v10i2.4
Short TitleA GENERAL ELLIPTIC NONLINEAR SYSTEM OF
Alternate JournalIeJPAM
Refereed DesignationRefereed