Geodesic
On the inverse problem of the calculus of variations for ordinary differential equations
Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 261-276.

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Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given.
DOI : 10.21136/MB.1993.125932
Classification : 49N45, 58E30, 58F05, 70H03, 70H35
Keywords: Lepagean forms; variational equations; Helmholtz conditions; minimal- order Lagrangian; local inverse problem to the calculus of variations; global inverse problem to the calculus of variations 
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Krupková, Olga. On the inverse problem of the calculus of variations for ordinary differential equations. Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 261-276. doi : 10.21136/MB.1993.125932. http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.125932/

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