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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 $\lambda$ and satisfying some additional continuity, compactness and growth conditions. The paper generalizes the result of [{\it 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:
 49J40 Variational methods including variational inequalities 58E05 Abstract critical point theory 35J20 Second order elliptic equations, variational methods 49J35 Minimax problems (existence)
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##### References:
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