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Complementary variational principles for a class of nonlinear boundary value problems

Published online by Cambridge University Press:  17 February 2009

N. Anderson  and
A. M. Arthurs
A. M. Arthurs
Affiliation:
Department of MathematicsUniversity of YorkYork, YO1 5DD, England
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Abstract

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Complementary variational principles are presented for a class of nonlinear boundary value problems S* Sφ = g(φ) in which g is not necessarily monotone. The results are illustrated by two examples, accurate variational solutions being obtained in both cases.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 1 , April 1979 , pp. 102 - 112
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Arthurs, A. M., “Extremum principles for a class of boundary value problems”, Proc. Camb. Phil. Soc. 65 (1969), 803–806.CrossRefGoogle Scholar
[2]Arthurs, A. M., Complementary variational principles (Clarendon Press, Oxford, 1970).Google Scholar
[3]Arthurs, A. M., “Dual extremum principles and error bounds for a class of boundary value problems”, J. Math. Anal. Appl. 41 (1973), 781–795.CrossRefGoogle Scholar
[4]Arthurs, A. M. and Winthrop, D., “Variational solution and error bound for a nonlinear boundary value problem in heat diffusion”, Nuovo Cimento Lett. 7 (1973), 150–152.CrossRefGoogle Scholar
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