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.
Recommended Citation
V. K. Le, "On Variational Inequalities with Maximal Monotone Operators and Multivalued Perturbing Terms in Sobolev Spaces with Variable Exponents," Journal of Mathematical Analysis and Applications, Elsevier, Jan 2012.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2011.09.058
Department(s)
Mathematics and Statistics
Keywords and Phrases
Subsolution; Supersolution; Multivalued Operator; Maximal Monotone Operator; Variational Inequality; Variable Exponent
International Standard Serial Number (ISSN)
0022-247X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2012 Elsevier, All rights reserved.
Publication Date
01 Jan 2012
