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

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.