### A new Morse theory and strong resonance problems

DOI: http://dx.doi.org/10.12775/TMNA.2003.005

#### Abstract

Is it possible to establish a new Morse theory if the function $f$ losses the (PS)

condition at some isolated values? Yes, it is! In this paper we will recall a such

a theory. One of the purposes of establishing such a theory is to consider multiplicity

results for strong resonance problems and to deal with multiple resonant energy levels.

Both of these questions were not studied much in the past because of the limitation of

methods. Using the new Morse theory we can deal with these problems.

condition at some isolated values? Yes, it is! In this paper we will recall a such

a theory. One of the purposes of establishing such a theory is to consider multiplicity

results for strong resonance problems and to deal with multiple resonant energy levels.

Both of these questions were not studied much in the past because of the limitation of

methods. Using the new Morse theory we can deal with these problems.

#### Keywords

Morse theory; strong resonance problems; elliptic boundary value problems

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