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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
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.
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