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.
"A new Morse theory and strong resonance problems." Topol. Methods Nonlinear Anal. 21 (1) 81 - 100, 2003.