Existence of Pulses for Monotone Reaction-Diffusion Systems

Abstract

Existence of pulse solutions, that is, positive stationary solutions with zero limit at infinity is studied for monotone reaction-diffusion systems in the bistable case. It is shown that such solutions exist if and only if the speed of the travelling wave described by the same system is positive. The proof is based on the Leray--Schauder method using topological degree for elliptic problems in unbounded domains and a priori estimates of solutions in some appropriate weighted spaces.