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.

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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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In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fractional order differential equations. The notions of classical and weak solutions are introduced. Then, existence results of at least one and three solutions are proved.MSC 2010 : Primary 34A08; Secondary 34B37, 58E05, 58E30, 26A33

Multiplicity results for a fourth-order nonlinear boundary value problem are presented. The proof of the main result is based on the critical point theory.

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