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The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations
Author(s):
M.
E.
Fels
Journal:
Trans. Amer. Math. Soc.
348
(1996),
5007-5029.
MSC (1991):
Primary 53B50, 49N45
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Abstract:
A simple invariant characterization of the scalar fourth-order 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 fourth-order equation through the application of Cartan's equivalence method. The solution to the inverse problem for fourth-order scalar equations provides the solution to an equivalence problem for second-order 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:
10.1090/S0002-9947-96-01720-5
PII:
S 0002-9947(96)01720-5
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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