Morse theory applied to semilinear problems

Abstract

We use Morse theoretic arguments to obtain nontrivial solutions of semilinear elliptic boundary value problems where the nonlinearity interacts with the spectrum, without assuming that the asymptotic limits at zero and infinity exist.

Keywords:

• semilinear elliptic boundary value problems
• nontrivial solutions
• Morse theory
• critical groups

AMS Subject Classification::

• 35J20