, Volume 57, Issue 2, pp 575-581
Date: 04 Nov 2012

An alternative proof of the mountain pass theorem for a class of functionals

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Abstract

We present an alternative proof of the Mountain Pass Theorem by means of the classical Ekeland Variational Principle for a class of \({\mathcal{C}^1}\) -functionals. In this new proof we avoid the machinery of convex analysis by a simpler characterization of the critical values of the functional.