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On a general nonlinear variational inequality

Published online by Cambridge University Press:  17 April 2009

Ramendra Krishna Bose
Ramendra Krishna Bose
Affiliation:
Department of Mathematics and Computer Science, State University of New York College at Fredonia, Fredonia NY 14063, United States of America
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Abstract

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Variational inequality theory provides techniques for solving a variety of applied problems in science and engineering. Recently Noor considered some interesting general nonlinear and linear variational inequalities in a series of papers and proved the existence and uniqueness of solutions by a fixed point technique developed by Glowinski, Lions and Tremolieres and also by a fixed point technique of Lions and Stampacchia. But there are several inaccuracies in his proofs and here they have been removed and correct formulation of the theorems are stated and proved and relationships are clearly shown. The existence of solution necessitates an additional condition in one case, and less condition in the other, but uniqueness can be proved without the condition that the operator be antimonotone.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 399 - 406
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Baiocchi, C. and Capelo, A., Variational and quasi-variational inequalities (Wiley, New York, London, 1984).Google Scholar
[2]Crank, J., Free and moving boundary probleme (Oxford University Press, United Kingdom, 1984).Google Scholar
[3]Duvaut, G. and Lions, J., Les inequations en mechanique et en physique (Dunod, Paris, 1972).Google Scholar
[4]Glowinski, R., Lions, J., and Tremolieres, R., Numerical analysis of variational inequalities (North Holland, Amsterdam, 1981).Google Scholar
[5]Noor, M. Aslam, ‘General nonlinear variational inequalities’, J. Math. Anal. Appl. 126 (1987), 78–84.CrossRefGoogle Scholar
[6]Noor, M. Aslam, ‘Variational inequalities related with a Signorini problem’, C.R. Math. Rep. Acad. Sci. Canada 7 (1985), 267–272.Google Scholar
[7]Lions, J. and Stampacchia, G., ‘Variational inequalities’, Comm. Pure Appl. Math. 20 (1967), 493–519.Google Scholar
[8]Noor, M. Aslam, ‘Variational inequalities for a class of contact problems with friction’, C.R. Math. Rep. Acad. Sci. Canada 5 (1983), 127–132.Google Scholar
[9]Noor, M. Aslam, ‘On a class of variational inequalities’, J. Math. Anal. Appl. 128 (1987), 138–155.CrossRefGoogle Scholar