On the inverse problem of the calculus of variations for ordinary differential equations

Olga Krupková

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 3, page 261-276
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Krupková, Olga. "On the inverse problem of the calculus of variations for ordinary differential equations." Mathematica Bohemica 118.3 (1993): 261-276. <http://eudml.org/doc/29086>.

@article{Krupková1993,
abstract = {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.},
author = {Krupková, Olga},
journal = {Mathematica Bohemica},
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; Lepagean forms; variational equations; Helmholtz conditions; minimal- order Lagrangian},
language = {eng},
number = {3},
pages = {261-276},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the inverse problem of the calculus of variations for ordinary differential equations},
url = {http://eudml.org/doc/29086},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Krupková, Olga
TI - On the inverse problem of the calculus of variations for ordinary differential equations
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 3
SP - 261
EP - 276
AB - 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.
LA - eng
KW - 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 forms; variational equations; Helmholtz conditions; minimal- order Lagrangian
UR - http://eudml.org/doc/29086
ER -

References

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