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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A resolution of the Euler operator. I


Authors: Peter J. Olver and Chehrzad Shakiban
Journal: Proc. Amer. Math. Soc. 69 (1978), 223-229
MSC: Primary 13N05; Secondary 49C10, 58F07
MathSciNet review: 486822
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Abstract: An exact sequence resolving the Elder operator of the calculus of variations for polynomial differential equations in one independent and one dependent variable is described. This resolution provides readily verifiable necessary and sufficient conditions for such a polynomial differential equation to be the Euler equation for some Lagrangian. An explicit construction of the Lagrangian is given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0486822-8
PII: S 0002-9939(1978)0486822-8
Keywords: Calculus of variations, Euler operator, Lagrangian, differential algebra
Article copyright: © Copyright 1978 American Mathematical Society