Volume 2,  Issue 2, 2001

Article 20

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

VY KHOI LE

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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On Some Fundamental Integral Inequalities and their Discrete Analogues
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Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements
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Monotonic Refinements of a Ky Fan Inequality
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Sub-super Solutions and the Existence of Extremal Solutions in Noncoercive Variational Inequalities
V.K. Le

Refinements of Carleman's Inequality
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Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals
I. Budimir, P. Cerone, and  J. Pecaric

Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
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Necessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
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Bounds for Entropy and Divergence for Distributions over a Two-Element Set
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