The authors prove a general theorem for the existence of at least three critical points for the functional being the sum of locally Lipschitz and convex, proper and lower semicontinuous functions on a separable, reflexive Banach space, depending on a real parameter and satisfying some additional continuity, compactness and growth conditions. The paper generalizes the result of [B. Ricceri, “On a three critical points theorem”, Arch. Math. 75, No. 3, 220-226 (2000; Zbl 0979.35040)].
Finally two applications of the above result are shown: one to a variational-hemivariational inequality and the other to an elliptic inequality problem with highly discontinuous nonlinearities.