A mountain pass theorem for a suitable class of functions

Abstract

The main purpose of this paper is to establish a three critical points result without assuming coercivity of the involved unctional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then pplied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions. Copyright © 2009 Rocky Mountain Mathematics Consortium.