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Journal of Convex Analysis 20 (2013), No. 1, 043--066
Copyright Heldermann Verlag 2013

Qualitative Stability of a Class of Non-Monotone Variational Inclusions. Application in Electronics

Samir Adly
XLIM UMR-CNRS 6172, Université de Limoges, 87060 Limoges, France

Jiri V. Outrata
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou vezí 4, 182 08 Prague, Czech Republic
and: Centre for Informatics and Applied Optimization, University of Ballarat, P. O. Box 663, Ballarat, Vic. 3353, Australia

The main concern of this paper is to investigate some stability properties (namely Aubin property and isolated calmness) of a special non-monotone variational inclusion. We provide a characterization of these properties in terms of the problem data and show their importance for the design of electrical circuits involving nonsmooth and non-monotone electronic devices like DIAC (DIode Alternating Current). Circuits with other devices like SCR (Silicon Controlled Rectifiers), Zener diodes, thyristors, varactors and transistors can be analyzed in the same way.

Keywords: Hemivariational inequalities, nonsmooth and variational analysis, Aubin property, isolated calmness, non-regular electrical circuits.

MSC: 46N10, 47N10, 47J20, 49J40, 34A60

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