Lepage forms,closed 2-forms and second-order ordinary differential equations |
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Authors: | O Krupková G E Prince |
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Institution: | (1) Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic;(2) La Trobe University, Bundoora, Victoria, 3086, Australia |
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Abstract: | Lepage 2-forms appear in the variational sequence as representatives of the classes of 2-forms. In the theory of ordinary
differential equations on jet bundles they are used to construct exterior differential systems associated with the equations
and to study solutions, and help to solve the inverse problem of the calculus of variations: since variational equations are
characterized by Lepage 2-forms that are closed. In this paper, a general setting for Lepage forms in the variational sequence
is presented, and Lepage 2-forms in the theory of second-order differential equations in general and of variational equations
in particular, are investigated in detail.
The text was submitted by the authors in English. |
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