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

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.

Keywords:

• critical set
• locally lipschitz continuous functions
• weak Palais–Smale condition

AMS Subject Classifications::

• Primary 58E05
• 49J35
• 49J52