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

*(English)*Zbl 1093.49005Summary: 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

##### MSC:

49J40 | Variational inequalities |

49K40 | Sensitivity, stability, well-posedness |

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

##### Keywords:

quasivariational inequalities; well-posedness; well-posedness in the generalized sense; set-valued mappings; fixed-points
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\textit{M. B. Lignola}, J. Optim. Theory Appl. 128, No. 1, 119--138 (2006; Zbl 1093.49005)

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##### References:

[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 |

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