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Existence of steady-state solutions for a one-predator-two-prey system. (English) Zbl 0705.92019
A one-predator, two (competing) prey situation is modelled by a three- dimensional system of elliptic partial differential equations, subject to Dirichlet boundary conditions. The existence of strictly positive solutions of the system is studied, and sufficient conditions are obtained, involving the parameters of the system, for such solutions to exist. The results are obtained by the use of degree theory in cones, positive operators and sub- and supersolution techniques.
Reviewer: J.H.Swart
MSC:
92D40Ecology
35J65Nonlinear boundary value problems for linear elliptic equations
92D25Population dynamics (general)