Well-posedness and \(L\)-well-posedness for quasivariational inequalities. (English) Zbl 1093.49005

Summary: In this paper, two concepts of well-posedness for quasivariational inequalities having a unique solution are introduced. Some equivalent characterizations of these concepts and classes of well-posed quasivariational inequalities are presented. The corresponding concepts of well-posedness in the generalized sense are also investigated for quasivariational inequalities having more than one solution


49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
47J20 Variational and other types of inequalities involving nonlinear operators (general)
Full Text: DOI


[2] Mosco, U., Implicit Variational Problems and Quasivariational Inequalities, Summer School, Nonlinear Operators and the Calculus of Variations, Bruxelles, Belgium, 1975; Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 543, pp. 83-156, 1976.
[15] Lignola, M. B., and Morgan, J., Approximate Solutions to Variational Inequalities and Applications: Equilibrium Problems with Side Constraints, Lagrangian Theory and Duality, Acireale, Italy, 1994, Le Mathematiche (Catania), Vol. 49, pp. 281–293, 1995. · Zbl 0848.49010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.