Electron. J. Diff. Equ., Vol. 2015 (2015), No. 265, pp. 1-10.

Semistability of first-order evolution variational inequalities

Hassan Saoud

Semistability is the property whereby the solutions of a dynamical system converge to a Lyapunov stable equilibrium point determined by the system initial conditions. We extend the theory of semistability to a class of first-order evolution variational inequalities, and study the finite-time semistability. These results are Lyapunov-based and are obtained without any assumptions of sign definiteness on the Lyapunov function. Our results are supported by some examples from unilateral mechanics and electrical circuits involving nonsmooth elements such as Coulomb's friction forces and diodes.

Submitted March 15, 2015. Published October 12, 2015.
Math Subject Classifications: 37C75, 49J40, 34G25.
Key Words: Lyapunov stability; semistability; finite-time semistability; evolution variational inequalities; complementarity problem; differential inclusions

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Hassan Saoud
Department of Mathematics, Lebanese University
Faculty of Sciences II,
P.O. Box 90656, Fanar-Matn, Lebanon
email: hassan.saoud@ul.edu.lb

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