On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems (Q5958913)

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 \(\lambda\) and satisfying some additional continuity, compactness and growth conditions. The paper generalizes the result of [\textit{B. Ricceri}, ``On a three critical points theorem'', Arch. Math. 75, No.~3, 220-226 (2000; Zbl 0979.35040)]. NEWLINENEWLINENEWLINEFinally 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.