An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model

摘要

The existence of travelling wave solutions of a diffusion reaction-system is studied via the generalized Morse index of isolated invariant sets. This index theory is analogous to degree theory, and the method of proof follows lines familiar from the latter theory. The equations in question are 'deformed' to a 'standard' system where the index can be easily computed, and the existence theorem follows from the 'non-triviality' of the index. The index theory has been described in other papers; here the main job is to construct 'isolating neighborhoods' which are analogous (in the degree theory) to open sets with no critical points on the boundary. Some novel means of location such neighborhoods are described.