A three critical points result in a bounded domain of a Banach space and applications

Abstract

Using the bounded mountain pass lemma and the Ekeland variational principle, we prove a bounded version of the Pucci-Serrin three critical points result in the intersection of a ball with a wedge in a Banach space. The localization constraints are overcome by boundary and invariance conditions. The result is applied to obtain multiple positive solutions for some semilinear problems.