Critical points for a class of nondifferentiable functions and applications

P. Candito; S. A. Marano; D. Motreanu

doi:10.3934/dcds.2005.13.175

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2005, Volume 13, Issue 1: 175-194. Doi: 10.3934/dcds.2005.13.175

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Critical points for a class of nondifferentiable functions and applications

1.
Dipartimento D.I.M.E.T., Università degli Studi Mediterranea di Reggio Calabria, Feo di Vito, 89100 Reggio Calabria
2.
Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari - Feo di Vito, 89100 Reggio Calabria
3.
Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex

Received: February 29, 2004

Revised: October 31, 2004

Published: March 2005

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Abstract

Some critical point theorems involving functionals that are the sum of a locally Lipschitz continuous term and of a convex, proper, besides lower semicontinuous, function are established. A recent existence result of Adly, Buttazzo, and Théra [1, Theorem 2.3] is improved. Applications to elliptic variational-hemivariational inequalities are then examined.

Keywords:

Critical points of non-smooth functions,
variational-hemivariational inequalities.

Mathematics Subject Classification: 49J40, 49J52, 35J85.

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