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Coexistence theorems of steady states for predator-prey interacting systems. (English) Zbl 0655.35021
The author gives necessary and sufficient conditions for the existence of positive solutions to the following system: \[ \Delta u+uM(u,v)=0,\quad d\Delta v+v(g(u)-m(v))=0,\quad (u,v)|_{\partial \Omega}=(0,0),\quad \Omega \subset {\mathbb{R}}\quad n, \] where M satisfies the so-called prey growth rate conditions, g and m are increasing functions satisfying \(g(0)-m(v)<0\) for v larger than some constant C. The paper includes many well-known systems and results as special cases, and some interesting examples are given.
Reviewer: C.F.Wang

MSC:
35J60 Nonlinear elliptic equations
92D25 Population dynamics (general)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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