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On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems. (English) Zbl 1014.49004

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 λ 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.


MSC:
49J40Variational methods including variational inequalities
58E05Abstract critical point theory
35J20Second order elliptic equations, variational methods
49J35Minimax problems (existence)