The generalized Conley index and multiple solutions of semilinear elliptic problems

Abstract

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.

Keywords

• Conley index
• elliptic equation
• critical point theory
• fixed point index
• superlinear problem.