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The multiplier problem of the calculus of variations for scalar ordinary differential equations

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Abstract

In the long-standing inverse problem of the calculus of variations one is asked to find a Lagrangian and a multiplier so that a given differential equation, after being multiplied with the multiplier, becomes the Euler–Lagrange equation for the Lagrangian. An answer to this problem for the case of a scalar ordinary differential equation of order \(2n, n\ge 2,\) is proposed.

Mathematics Subject Classification

49N45 53B50 (35K25) 

Notes

Acknowledgements

The author is deeply indebted to his M.Phil. advisor Prof. Kai-Seng Chou for suggesting this problem, as well as carefully reviewing the first draft of this article and giving numerous valuable suggestions. The author also thanks Prof. Kai-Seng Chou for his continuous support, while and after pursuing his master degree at The Chinese University of Hong Kong. The author also thanks the anonymous referee for the very useful comments.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of British ColumbiaVancouverCanada

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