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Sufficient conditions in the problem of Lagrange without assumptions of normalcy


Author: Marston Morse
Journal: Trans. Amer. Math. Soc. 37 (1935), 147-160
MSC: Primary 49K05
DOI: https://doi.org/10.1090/S0002-9947-1935-1501780-9
MathSciNet review: 1501780
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  • [1] Bolza, Über den ``anormalen Fall'' beim Lagrangeschen und Mayerschen Problem mit gemischten Bedingungen und variablen Endpunkten, Mathematische Annalen, vol. 74 (1913), pp. 430-446. MR 1511773
  • [2] Bliss, The problem of Bolza in the calculus of variations, Annals of Mathematics, vol. 33 (1932), pp. 261-274. MR 1503050
  • [3] Carathéodory, Üeber die Einteilung der Variationsprobleme von Lagrange nach Klassen, Commentarii Mathematici Helvetici, vol. 5 (1933), pp. 1-19. MR 1509462
  • [4] Hestenes, Sufficient conditions for the problem of Bolza in the calculus of variations, these Transactions, vol. 35 (1934).
  • [5] Currier, The variable end point problem of the calculus of variations including a generalization of the classical Jacobi conditions, these Transactions, vol. 34 (1932), pp. 689-704. MR 1501657
  • [6] Morse and Myers, The problems of Lagrange and Mayer with variable end points, Proceedings of the American Academy of Arts and Sciences, vol. 66 (1931), pp. 235-253.
  • [7] Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Annals of Mathematics, vol. 32 (1931), pp. 567-577. MR 1503017
  • [8] Morse, Sufficient conditions in the problem of Lagrange with variable end points, American Journal of Mathematics, vol. 53 (1931), pp. 517-546.
  • [9] Note added in proof. At the September meeting of the Society at Williamstown, Dr. Reid, unaware of the existence of the present paper, reported on a proof of theorems similar to the theorems contained herein. In the final theorems he assumed normalcy on the interval $ ({a^1},{a^2})$ as against the author's weaker assumption that a $ {\lambda _0}$ exists which is not zero. More recently Dr. Hestenes has announced proofs of the theorems concerned.

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DOI: https://doi.org/10.1090/S0002-9947-1935-1501780-9
Article copyright: © Copyright 1935 American Mathematical Society

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