# American Institute of Mathematical Sciences

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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

 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.
Citation: Roberto Livrea, Salvatore A. Marano. A min-max principle for non-differentiable functions with a weak compactness condition. Communications on Pure &amp; Applied Analysis, 2009, 8 (3) : 1019-1029. doi: 10.3934/cpaa.2009.8.1019
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