Stability and Existence Results for Quasimonotone Quasivariational Inequalities in Finite Dimensional Spaces

Journal Article · Mon Feb 15 00:00:00 EST 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-015-9296-2· OSTI ID:22469613

Castellani, Marco; Giuli, Massimiliano ^[1]

---

1. University of L’Aquila, Department of Information Engineering, Computer Science and Mathematics (Italy)

We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered.

• OSTI ID: 22469613
• Journal Information: Applied Mathematics and Optimization, Vol. 73, Issue 1; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
NETWORK ANALYSIS
STABILITY