Bounded Palais-Smale sequences for functionals with a mountain pass geometry

摘要

We prove the existence of bounded Palais-Smale sequences for abstract functionals with a mountain pass geometry under hypotheses weaker than those commonly used in the literature. This is obtained via a generalization of a generic result of Jeanjean, combined with a rescaling argument. Applications to the existence of nontrivial solutions to semilinear elliptic problems are given.