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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MR Zbl
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.
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 
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
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