The inverse problem of the calculus of variations for scalar fourthorder ordinary differential equations
Author:
M. E. Fels
Journal:
Trans. Amer. Math. Soc. 348 (1996), 50075029
MSC (1991):
Primary 53B50, 49N45
MathSciNet review:
1373634
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Abstract: A simple invariant characterization of the scalar fourthorder ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier are expressed in terms of the vanishing of two relative invariants which can be associated with any fourthorder equation through the application of Cartan's equivalence method. The solution to the inverse problem for fourthorder scalar equations provides the solution to an equivalence problem for secondorder Lagrangians, as well as the precise relationship between the symmetry algebra of a variational equation and the divergence symmetry algebra of the associated Lagrangian.
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Additional Information
M. E. Fels
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
fels@math.umn.edu
DOI:
http://dx.doi.org/10.1090/S0002994796017205
PII:
S 00029947(96)017205
Keywords:
Inverse problem of the calculus of variations,
variational principles for scalar ordinary differential equations,
variational bicomplex,
equivalence method,
divergence symmetries
Received by editor(s):
June 15, 1995
Article copyright:
© Copyright 1996
American Mathematical Society
