A min-max principle for non-differentiable functions with a weak compactness condition

Roberto Livrea; Salvatore A. Marano

doi:10.3934/cpaa.2009.8.1019

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2009, Volume 8, Issue 3: 1019-1029. Doi: 10.3934/cpaa.2009.8.1019

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A min-max principle for non-differentiable functions with a weak compactness condition

Roberto Livrea^1, and
Salvatore A. Marano^2,

1.
Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari, 89100 Reggio Calabria
2.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania

Received: February 29, 2008

Revised: December 31, 2008

Published: April 2009

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Abstract

A general critical point result established by Ghoussoub is extended to the case of locally Lipschitz continuous functions satisfying a weak Palais-Smale hypothesis, which includes the so-called non-smooth Cerami condition. Some special cases are then pointed out.

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Mathematics Subject Classification: Primary: 58E05, 49J35, 49J52.

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