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The Relationships Between Equilibria and Positive Solutions of Certain Nonlinear Elliptic Systems

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
209
Issue
1
Identifiers
DOI: 10.1006/jmaa.1997.5354

Abstract

Abstract Let M( u, v) = 0, N( u, v) = 0 define two distinct phase curves Γ 1, Γ 2in 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 Δu + uM(u, v) = 0, Δv + vN(u, v) = 0 in Ω ⊂ R n under Dirichlet boundary conditions, where Ω is a bounded domain and M, Nare monotone functions.

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