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.
International Electronic Journal of Pure and Applied Mathematics
Robertson, Timothy and Hyuk Kang, Joon, "A General Elliptic Nonlinear System of Multiple Functions with Application" (2016). Faculty Publications. 270.
Retrieved March 29, 2018, from http://www.e.ijpam.eu/contents/articles/201601002004.pdf