EXISTENCE OF POSITIVE STATIONARY SOLUTIONS AND THRESHOLD RESULTS FOR A REACTION-DIFFUSION SYSTEM

The system u(1t) - Delta u(1) = u(1)u(2) - bu(1), u(2t) - Delta u(2) = au(1) in Omega x (0, T), where Omega subset of R(n) is a smooth bound ed domain, with homogeneous Dirichlet boundary conditions u(1) = u(2) = 0 on partial derivative Omega x (0, T) and initial conditions u(1)(x , 0), u(2)(x, 0), is studied. First, it is proved that there is at lea st one positive stationary solution if 2 less than or equal to n<6. Se cond, it is proved that every positive stationary solution is a thresh old when Omega is a ball. (C) 1996 Academic Press. Inc.