On Variational and Quasi-variational Inequalities with Multivalued Lower Order Terms and Convex Functionals
Carl, Siegfried and Mitidieri, Enzo Luigi
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 Ju are convex functionals, and Ju 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.
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
Mathematics and Statistics
Keywords and Phrases
Variational Inequality; Quasi-variational Inequality; Subsolution; Supersolution; Multivalued Operator
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