Title

On Variational Inequalities with Maximal Monotone Operators and Multivalued Perturbing Terms in Sobolev Spaces with Variable Exponents

Editor(s)

Aron, Richard M. and Chen, Goong and Krantz, Steven G.

Abstract

We are concerned in this paper with variational inequalities of the form: {A(u), v-u)+(F(u),v-u)≥(L,v-u), VѵϵK, uϵK,} where A is a maximal monotone operator, F is an integral multivalued lower order term, and K is a closed, convex set in a Sobolev space of variable exponent. We study both coercive and noncoercive inequalities. In the noncoercive case, a sub-supersolution approach is followed to obtain the existence and some other qualitative properties of solutions between sub- and supersolutions.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Subsolution; Supersolution; Multivalued Operator; Maximal Monotone Operator; Variational Inequality; Variable Exponent

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2012 Elsevier, All rights reserved.

Share

 
COinS