an:01031560
Zbl 0884.35032
Li, Lige; Cao, Guoxiang; Liu, Yaping
The relationships between equilibria and positive solutions of certain nonlinear elliptic systems
EN
J. Math. Anal. Appl. 209, No. 1, 154-179 (1997).
00041662
1997
j
35J55 35J60 92D25
predation; competition; positive equilibria
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.
C.Y.Chan (Lafayette)