Abstract and Applied Analysis
Volume 1 (1996), Issue 1, Pages 103-135
The generalized Conley index and multiple solutions of semilinear elliptic problems
1School of Mathematics and Statistics, University of Sydney, Sydney 2006, NSW, Australia
2Department of Mathematics, Statistics and Computer Science, University of New England, Armidale 2351, NSW, Australia
Received 22 February 1996
Copyright © 1996 E. N. Dancer and Yihong Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish some framework so that the generalized Conley
index can be easily used to study the multiple solution problem of semilinear elliptic
boundary value problems. Both the parabolic flow and the gradient
flow are used. Some examples are given to compare our approach here with
other well-known methods. Our abstract results with parabolic flows may
have applications to parabolic problems as well.