Sub-super Solutions and the Existence of Extremal Solutions in Noncoercive Variational Inequalities

Volume 2, Issue 2, 2001

Article 20

SUB-SUPER SOLUTIONS AND THE EXISTENCE OF EXTREMAL SOLUTIONS IN NONCOERCIVE VARIATIONAL INEQUALITIES

DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MISSOURI-ROLLA
ROLLA, MO 65409, USA
E-Mail: vy@umr.edu

Received 13 September, 2000; accepted 28 February, 2001.
Communicated by: A.M. Rubinov

ABSTRACT. The paper is concerned with the solvability of variational inequalities that contain second-order quasilinear elliptic operators and convex functionals. Appropriate concepts of sub- and supersolutions (for inequalities) are introduced and existence of solutions and extremal solutions are discussed.

Key words:
subsolution, supersolution, extremal solution, variational inequality.

2000 Mathematics Subject Classification:
35J25, 35J60, 35J65, 35J85

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