Download or read book An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model written by Charles C. Conley and published by . This book was released on 1980 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.