Abstract and Applied Analysis
Volume 1 (1996), Issue 1, Pages 103-135

The generalized Conley index and multiple solutions of semilinear elliptic problems

E. N. Dancer1 and Yihong Du2

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.