The relationships between equilibria and positive solutions of certain nonlinear elliptic systems

[摘要] 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, Delta v + vN(u, v) = 0 in Omega subset of R-n under Dirichlet boundary conditions, where Omega is a bounded domain and M, N are monotone functions. (C) 1997 Academic Press.

[发布日期] 1997-05-01