On Variational and Quasi-variational Inequalities with Multivalued Lower Order Terms and Convex Functionals

Author

Vy Khoi Le, Missouri University of Science and TechnologyFollow

Editor(s)

Carl, Siegfried and Mitidieri, Enzo Luigi

Abstract

In this paper, we consider the existence and some qualitative properties of solutions of variational inequalities of the form: and of quasi-variational inequalities of the form: where a is a second-order elliptic operator of Leray–Lions type, F is a multivalued lower order term, J and J_u are convex functionals, and J_u also depends on u. We concentrate here in noncoercive cases and use sub-supersolution methods to study the existence and enclosure of solutions, and also the existence of extremal solutions between sub and supersolutions.

Recommended Citation

V. K. Le, "On Variational and Quasi-variational Inequalities with Multivalued Lower Order Terms and Convex Functionals," Nonlinear Analysis: Theory, Methods and Applications, Elsevier, Jan 2014.

The definitive version is available at https://doi.org/10.1016/j.na.2013.07.034

Department(s)

Mathematics and Statistics

Keywords and Phrases

Variational Inequality; Quasi-variational Inequality; Subsolution; Supersolution; Multivalued Operator

International Standard Serial Number (ISSN)

0362-546X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 Elsevier, All rights reserved.

Publication Date

01 Jan 2014