The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.
Multiple critical points theorems for non-differentiable functionals are established. Applications both to elliptic variational-hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented.
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