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Full-Text Articles in Physical Sciences and Mathematics
A General Elliptic Nonlinear System Of Multiple Functions With Application, Timothy Robertson, Joon Hyuk Kang
A General Elliptic Nonlinear System Of Multiple Functions With Application, Timothy Robertson, Joon Hyuk Kang
Faculty Publications
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 …
A General Elliptic Nonlinear System Of Two Functions With Application, Timothy Robertson, Joon Hyuk Kang
A General Elliptic Nonlinear System Of Two Functions With Application, Timothy Robertson, Joon Hyuk Kang
Faculty Publications
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 …