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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 1
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Original Articles

On the structure of the critical set of non-differentiable functions with a weak compactness condition

Gabriele Bonanno Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, 98166 Messina, ItalyCorrespondence[email protected]
&
Salvatore A. Marano Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy
Pages 1-10 | Received 17 Mar 2009, Accepted 09 Sep 2009, Published online: 19 Jan 2010
 
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Abstract

The nature of critical points generated by a Ghoussoub's type min–max principle for locally Lipschitz continuous functionals fulfilling a weak Palais–Smale assumption, which contains the so-called non-smooth Cerami condition, is investigated. Two meaningful special cases are then pointed out; see Theorems 3.5 and 3.6.

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