Monotone penalty approximation of extremal solutions for quasilinear noncoercive variational inequalities
 Citation data:

Nonlinear Analysis: Theory, Methods & Applications, ISSN: 0362546X, Vol: 57, Issue: 2, Page: 311322
 Publication Year:
 2004

 EBSCO 4
 Bepress 1

 EBSCO 2
 Repository URL:
 http://scholarsmine.mst.edu/math_stat_facwork/296
 DOI:
 10.1016/j.na.2004.02.015
 Author(s):
 Publisher(s):
 Tags:
 Mathematics; extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; subsupersolutions; variational inequalities; extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; subsupersolutions; 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 lowerorder term F is imposed.