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Zbl 1014.49004
Marano, Salvatore A.; Motreanu, Dumitru
On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 48, No.1, A, 37-52 (2002). ISSN 0362-546X

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)]. \par 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.
[Leszek Gasiński (Kraków)]

MSC 2000:: *49J40 Variational methods including variational inequalities
58E05 Abstract critical point theory
35J20 Second order elliptic equations, variational methods
49J35 Minimax problems (existence)

Keywords: critical points; variational-hemivariational inequality; elliptic eigenvalue problem

Citations: Zbl 0979.35040

Cited in: Zbl 1221.49008

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