Volume 4, Number 2, Spring 1996
POSITIVE STEADY-STATES FOR LARGE SYSTEMS
OF REACTION-DIFFUSION EQUATIONS:
SYNTHESIZING FROM SMALLER SUBSYSTEMS
ANTHONY W. LEUNG AND LUIS A. ORTEGA
Abstract. Large systems of reaction-diffusion equations
describing many interaction species are studied. In each
case, two uncoupled related subsystems are constructed and
analyzed. It is shown that appropriate properties of the
subsystems will insure that the full system has a steady-state
solution which is strictly positive in each component. The
problem is applicable to the study of the coexistence of all
species when two subgroups of species are mixed together.
The method of bifurcation and upper-lower solutions are used
in the analysis. Bifurcation theory is used in the construction
of lower solutions.