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

Let M u,¨.s0, N u,¨.s0 define two distinct phase curves G1, G2 in the u,¨.-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 DuquM u, ¨.s0, D¨ q¨N u,¨.s0 inV;Rn under Dirichlet boundary conditions, where V is a bounded domain and M, N are monotone functions