Multiple solutions of hemivariational inequalities with area-type term

Abstract

Hemivariational inequalities containing both an area-type and a non-locally Lipschitz term are considered. Multiplicity results are obtained by means of techniques of nonsmooth critical point theory. Mathematics Subject Classification (1991): 35J85 Recalls of nonsmooth analysisLet X be a metric space endowed with the metric d and let f : X → R be a function. We denote by B r (u) the open ball of centre u and radius r and we set

Unbounded critical points for a class of lower semicontinuous functionals

“…We apply a nonsmooth critical point theory developed in [10,12,13] and applied in [8,9,20] to treat the case of continuous functionals. r 2004 Elsevier Inc. All rights reserved.…”

Linking solutions for quasilinear equations at critical growth involving the “1-Laplace” operator

“…A first idea could be to apply the approach of Chang [8] to the locally Lipschitz functional f defined on BV ( ). However, it has been already observed that, in such a setting, the Palais-Smale condition fails even in the subcritical case, as the norm-convergence of BV cannot be usually obtained for a Palais-Smale sequence (see Marzocchi [29] and Degiovanni et al [15]). For this reason, it is more convenient to extend the functional f to L 1 * ( ) with value +∞ outside BV ( ).…”

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“…In this way the functional becomes only lower semicontinuous, but one can recover the Palais-Smale condition. We refer the reader to [12,14,21,24] for results in this direction.…”