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Marano, Salvatore A.; Mosconi, Sunra J. N.

Non-smooth critical point theory on closed convex sets. (English) Zbl 1286.58008

Commun. Pure Appl. Anal. 13, No. 3, 1187-1202 (2014).
Summary: A critical point theory for non-differentiable functionals defined on a closed convex subset of a Banach space is worked out. Special attention is paid to the notion of critical point and possible compactness conditions of Palais-Smale’s type. Two Mountain-Pass like theorems are also established. Concepts and results are compared with those already existing in the literature.

Cited in 3 Documents

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49J35 Existence of solutions for minimax problems
49J52 Nonsmooth analysis

Keywords:

critical point; weak Palais-Smale condition; min-max theorem; functional defined on a closed convex set; non-smooth function
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References:

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