A three critical point theorem for non-smooth functionals with application in differential inclusions

A variety of three-critical-point theorems have been established for non-smooth functionals, based on a minimax inequality. In this paper, a generalized form of a recent result due to Ricceri is introduced for non-smooth functionals and by a few hypotheses, without any minimax inequality, the existence of at least three critical points with a uniform bound on the norms of solutions, is obtained. Also, as an application, our main theorem is used to obtain at least three anti-periodic solutions for a second order differential inclusion.