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A direct sufficiency proof for the problem of Bolza in the calculus of variations


Author: Magnus R. Hestenes
Journal: Trans. Amer. Math. Soc. 42 (1937), 141-154
MSC: Primary 49K05
DOI: https://doi.org/10.1090/S0002-9947-1937-1501917-3
MathSciNet review: 1501917
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  • [I] Bliss, The problem of Lagrange in the calculus of variations, American Journal of Mathematics, vol. 52 (1930), pp. 673-744. MR 1506783
  • [II] Morse, Sufficient conditions in the problem of Lagrange with variable end points, American Journal of Mathematics, vol. 53 (1931), pp. 517-596.
  • [III] Bliss, The problem of Bolza in the calculus of variations, Annals of Mathematics, (2), vol. 33 (1932), pp. 261-274. MR 1503050
  • [IV] Hestenes, Sufficient conditions for the problem of Bolza in the calculus of variations, these Transactions, vol. 36 (1934), pp. 793-818. MR 1501767
  • [V] Morse, Sufficient conditions in the problem of Lagrange without assumptions of normalcy, these Transactions, vol. 37 (1935), pp. 147-160. MR 1501780
  • [VI] Reid, The theory of the second variation for the non-parametric problem of Bolza, American Journal of Mathematics, vol. 57 (1935), pp. 573-586. MR 1507097
  • [VII] Bliss, The problem of Bolza in the calculus of variations, Lectures delivered at the University of Chicago during the Winter Quarter, 1935.
  • [VIII] Hestenes, On sufficient conditions in the problems of Lagrange and Bolza, Annals of Mathematics, (2), vol. 37 (1936), pp. 543-551. MR 1503298
  • [IX] Reid, Sufficient conditions by expansion methods for the problem of Bolza in the calculus of variations in parametric form, Bulletin of the American Mathematical Society, vol. 41 (1935), p. 788, abstract 41-11-379.

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DOI: https://doi.org/10.1090/S0002-9947-1937-1501917-3
Article copyright: © Copyright 1937 American Mathematical Society

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