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A GENERAL ELLIPTIC NONLINEAR SYSTEM OF TWO FUNCTIONS WITH APPLICATION

TitleA GENERAL ELLIPTIC NONLINEAR SYSTEM OF TWO FUNCTIONS WITH APPLICATION
Publication TypeJournal Article
Year of Publication2016
AuthorsRobertson, T, Kang, JHyuk
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume10
Issue2
Start Page115
Pagination12
Date Published10/2016
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
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.
URLhttp://www.e.ijpam.eu/contents/articles/201601002002.pdf
DOI10.12732/iejpam.v10i2.2
Short TitleA GENERAL ELLIPTIC NONLINEAR SYSTEM
Alternate JournalIeJPAM
Refereed DesignationRefereed