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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] I. M. Gel′fand and L. A. Dikiĭ, Asymptotic properties of the resolvent of Sturm-Liouville equations, and the algebra of Korteweg-de Vries equations, Uspehi Mat. Nauk 30 (1975), no. 5(185), 67–100 (Russian). MR 0508337
  • [2] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325

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Keywords: Calculus of variations, Euler operator, Lagrangian, differential algebra
Article copyright: © Copyright 1978 American Mathematical Society