Taiwanese Journal of Mathematics

ON THE PALAIS-SMALE CONDITION FOR NONDIFFERENTIABLE FUNCTIONALS

Hong-Kun Xu

Full-text: Open access

Abstract

Two kinds of Palais-Smale condition, $(PS)_c$ and $(PS)^*_c$, for nondifferentiable functionals are studied. It is shown that $(PS)_c$ implies $(PS)^*_c$ and that they are equivalent for convex functionals. This points out a gap in the proof of Costa and Goncalves [5, Proposition 3]. Some other nonsmooth versions of known smooth results are also obtained.

Article information

Source
Taiwanese J. Math., Volume 4, Number 4 (2000), 627-634.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407296

Digital Object Identifier
doi:10.11650/twjm/1500407296

Mathematical Reviews number (MathSciNet)
MR1799757

Zentralblatt MATH identifier
0988.49009

Subjects
Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 58E30: Variational principles 58C20: Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]

Keywords
Palais-Smale condition nondifferentiable functional generalized derivative Clarke's differential critical point Ekeland's Principle

Citation

Xu, Hong-Kun. ON THE PALAIS-SMALE CONDITION FOR NONDIFFERENTIABLE FUNCTIONALS. Taiwanese J. Math. 4 (2000), no. 4, 627--634. doi:10.11650/twjm/1500407296. https://projecteuclid.org/euclid.twjm/1500407296


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