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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A range and existence theorem for pseudomonotone perturbations of maximal monotone operators


Author: Vy Khoi Le
Journal: Proc. Amer. Math. Soc. 139 (2011), 1645-1658
MSC (2010): Primary 35J85, 47H05, 47J20, 47J30
Published electronically: September 3, 2010
MathSciNet review: 2763754
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Abstract: In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.


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Additional Information

Vy Khoi Le
Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409
Email: vy@mst.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10594-4
PII: S 0002-9939(2010)10594-4
Received by editor(s): March 9, 2010
Received by editor(s) in revised form: May 10, 2010
Published electronically: September 3, 2010
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society