Homotopical properties of a class of nonsmooth functions

Summary A class of extended real valued functionals, already considered for evolution problems, is studied. The set where the functional is finite is proved to be an absolute neighborhood extensor. Applications to critical point theory, involving Ljusternik-Schnirelman category and cohomological index, are shown. The stability under -convergence of the homotopical type of the sublevels of the functional is also treated.The author is a member of theGruppo Nazionale per l'Analisi Funzionalc e le sue Applicazioni (C.N.R.).