
The celebrated mountain pass principle of Ambrosetti and Rabinowitz is one of the most important tools in nonlinear analysis for proving the existence of critical points of \(C^1\) real functionals. The authors establish in this paper a general mountain pass principle, dropping any smoothness or even continuity assumptions on the functional. The classical Fréchet differential is replaced by the weak slope, in the sense defined by Degiovanni, and the basic tool in the proof is a nonsmooth version of the deformation lemma. As a corollary of the main result the authors deduce the existence of a point with an arbitrarily small slope if the ``low'' part of the ``barrier'' is sufficiently far from the ``boundary'', obtaining in addition estimates for the location of the point.
intrinsic, mountain pass principle, weak slope, nonsmooth analysis, variational methods, critical point, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Variational principles in infinite-dimensional spaces, complete metric space, Variational problems in a geometric measure-theoretic setting, deformation lemma
intrinsic, mountain pass principle, weak slope, nonsmooth analysis, variational methods, critical point, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Variational principles in infinite-dimensional spaces, complete metric space, Variational problems in a geometric measure-theoretic setting, deformation lemma
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