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Complementary variational principles for a class of differential equations

Published online by Cambridge University Press:  24 October 2008

A. M. Arthurs
Affiliation:
Department of Mathematics, University of York
C. W. Coles
Affiliation:
Department of Mathematics, University of York

Abstract

Maximum and minimum principles for certain ordinary differential equations of order 2m are derived in a unified manner from the theory of complementary variational principles for multiple operator equations. The minimum principle is known in the literature, but the maximum principle appears to be new.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Mikhlin, S. G. and Smolitskiy, K. L.Approximate methods for solution of differential and integral equations, p. 178 (American Elsevier Pub. Co. Inc., New York, 1967).Google Scholar
(2)Shampine, L. F.Error bounds and variational methods for nonlinear boundary value problems. Numer. Math. 12 (1968), 410415.CrossRefGoogle Scholar
(3)Arthurs, A. M.Complementary variational principles (Clarendon Press, Oxford, 1970).Google Scholar
(4)Arthurs, A. M.A note on Komkov's class of boundary value problems and associated variational principles. J. Math. Anal. Appl. 33 (1971), 402407.CrossRefGoogle Scholar
(5)Arthurs, A. M. and Coles, C. W.Error bounds and variational methods for nonlinear differential and integral equations, J. Inst. Math. Appl. 7 (1971), 324330.CrossRefGoogle Scholar