The authors study the nature of critical points for locally Lipschitz continuous functionals satisfying a non-smooth Cerami condition. Critical points are obtained via min-max results under Ghoussoub’s type linking conditions. Their results rely on Theorem 3.1 of R. Livrea and S. A. Marano [Commun. Pure Appl. Anal. 8, No. 3, 1019–1029 (2009; Zbl 1208.58014)].
Assuming the existence of two local minimums (and other suitable hypotheses), the existence of a third critical point which is not a local minimum is established. This last result is applied to obtain the existence of three critical points of functionals of the form: , with a real parameter, and sequentially weakly lower semi-continuous.