A variant of mountain-pass theorem. (Q2249886)

The authors establish a version of the mountain-pass theorem, in which the functional involved satisfies a cut-off Palais-Smale condition, weaker than the classical one (Theorem 2.1). They show that either the critical point is not a local minimum or the functional admits a sequence of distinct local minima. They obtain also a multiplicity result of critical points (Theorem 2.3) and give a precise localization of them. Finally, they present an application to a two-point boundary value problem, and obtain a precise estimate of the \(L^{\infty }\) norm of the solutions.