Bounded Palais-Smale mountain-pass sequences
Abstract
Let I(lambda, .), lambda is an element of R, be a family of C-1-functionals having mountain-pass geometry. Under hypotheses which do not ensure that the mountain-pass level c(lambda) is a monotone function of lambda, it is shown that I(lambda, .) has a bounded Palais-Smale sequence at level c(lambda), for almost every lambda. (C) Academie des Sciences/Elsevier, Paris.