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The relationships between equilibria and positive solutions of certain nonlinear elliptic systems. (English) Zbl 0884.35032
Author’s abstract: Let $$M(u,v)=0$$, $$N(u,v)=0$$ define two distinct phase curves $$\Gamma_1$$, $$\Gamma_2$$ in the $$(u,v)$$-phase plane. This paper presents results on the relationships among the positive equilibria, the phase curves, and the existence of positive solutions to the PDE system $\Delta u+uM(u,v)=0, \quad \Delta v+vN(u,v)=0 \quad \text{in } \Omega \subset \mathbb{R}^n$ under Dirichlet boundary conditions, where $$\Omega$$ is a bounded domain and $$M,N$$ are monotone functions.

##### MSC:
 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J60 Nonlinear elliptic equations 92D25 Population dynamics (general)
##### Keywords:
predation; competition; positive equilibria
Full Text:
##### References:
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