ON LIPSCHITZ STABILITY OF A CLASS OF EXTENDED REAL-VALUED HEMIVARIATIONAL INEQUALITIES – APPLICATION TO A NONSMOOTH BOUNDARY VALUE PROBLEM

Mohamed Ait Mansour^†, Joachim Gwinner^‡, Zakaria Mazgouri^§

Abstract: In this paper, we first present a sensitivity analysis for extended real-valued hemivariational inequalities and variational–hemivariational inequalities in reflexive Banach spaces. In particular, we provide estimates of Lipschitz type with respect to parametric perturbations in the elliptic operator and the Clarke directional derivative. Then, we apply our quantitative stability result to an elliptic scalar boundary value problem that models unilateral contact problems in solid mechanics with nonmonotone friction.

Keywords: sensitivity analysis, extended real-valued equilibria, hemivariational inequality, Clarke subdifferential, unilateral contact problem, non-monotone friction.

MSC: 49J40, 49J53, 49K40, 35J66, 47J20, 47J22.

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DOI 10.56082/annalsarscimath.2026.1.179

^†ait.mansour.mohamed@gmail.com, LP2EA Laboratory, Department of Physics, Polydisciplinary Faculty, Cadi Ayyad University, Safi, Morocco
^‡joachim.gwinner@unibw-muenchen.de, Institute of Applied Mathematics, Department of Aerospace Engineering, Universität der Bundeswehr München, Germany
^§zakaria.mazgouri@usmba.ac.ma, ORCID 0000-0003-0131-4741, LSATE Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, 30000 Fez, Morocco

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 1, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997