Monotone penalty approximation of extremal solutions for quasilinear noncoercive variational inequalities

Citation data:

Nonlinear Analysis: Theory, Methods & Applications, ISSN: 0362-546X, Vol: 57, Issue: 2, Page: 311-322

Publication Year:
2004
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Repository URL:
http://scholarsmine.mst.edu/math_stat_facwork/296
DOI:
10.1016/j.na.2004.02.015
Author(s):
Le, Vy Khoi; Carl, Siegfried
Publisher(s):
Elsevier BV; Elsevier
Tags:
Mathematics; extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; sub-supersolutions; variational inequalities; extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; sub-supersolutions; variational inequalities; Statistics and Probability
article description
This paper is about a monotone approximation scheme for extremal (least or greatest) solutions of the following variational inequality: u∈K:〈Au+F(u),v−u〉⩾0,∀v∈K, in the interval between some appropriately defined sub- and supersolutions. The variational inequality is approximated by a sequence of penalty equations. The extremal solutions of the penalty equations, constructed iteratively and forming a monotone sequence, are proved to converge to the corresponding solutions of the original inequality. We note that no monotoneity assumption on the lower-order term F is imposed.