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.
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Montenegro, M., Presoto, A.E. An alternative proof of the mountain pass theorem for a class of functionals. J Glob Optim 57, 575–581 (2013). https://doi.org/10.1007/s10898-012-0001-6
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DOI: https://doi.org/10.1007/s10898-012-0001-6