Existence of coupled quasi-solutions of systems of nonlinear reaction- diffusion equations (Q1074022)

We investigate general systems of nonlinear reaction-diffusion problems when the nonlinear terms possess a mixed quasi-monotone property. We discuss a very general situation and obtain coupled extremal quasi- solutions, which in special cases reduce to minimal and maximal solutions. We shall also indicate how one-step cyclic monotone iterative schemes can be generated which yield accelerated rate of convergence of iterates. This work is in the spirit of our recent paper [Nonlinear Anal., Theory Methods Appl. 8, 501-515 (1984; Zbl 0575.35033)] for elliptic systems.