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May  2009, 8(3): 1019-1029. doi: 10.3934/cpaa.2009.8.1019

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, Italy
2. 

Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy

Received  March 2008 Revised  January 2009 Published  February 2009

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.
Keywords: Mountain Pass geometry., Critical points, locally Lipshitz continuous functions, weak Palais-Smale condition.
Mathematics Subject Classification: Primary: 58E05, 49J35, 49J5.
Citation: Roberto Livrea, Salvatore A. Marano. A min-max principle for non-differentiable functions with a weak compactness condition. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1019-1029. doi: 10.3934/cpaa.2009.8.1019
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