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On operator equations and variational principles

Published online by Cambridge University Press:  24 October 2008

A. M. Arthurs
A. M. Arthurs
Affiliation:
Department of Mathematics, University of York
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Abstract

A necessary and sufficient condition for operator equations Tϕ = M(u, ϕ), T*u = N(u, ϕ) to arise from a variational principle is presented.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 277 - 279
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Arthurs, A. M.Complementary variational principles (Clarendon Press; Oxford, 1970).Google Scholar
(2)Rall, L. B.On complementary variational principles, J. Math. Anal. Appl. 14 (1966), 174–184.CrossRefGoogle Scholar
(3)Vainberg, M. M.Variational methods for the study of non-linear operator equations (Holden-Day, San Francisco, 1963).Google Scholar