Sufficient conditions in the problem of Lagrange without assumptions of normalcy
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- by Marston Morse PDF
- Trans. Amer. Math. Soc. 37 (1935), 147-160 Request permission
References
- Oskar Bolza, Über den ”Anormalen Fall” beim Lagrangeschen und Mayerschen Problem mit gemischten Bedingungen und variablen Endpunkten, Math. Ann. 74 (1913), no. 3, 430–446 (German). MR 1511773, DOI 10.1007/BF01456753
- Gilbert Ames Bliss, The problem of Bolza in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 2, 261–274. MR 1503050, DOI 10.2307/1968328
- C. Carathéodory, Ueber die Einteilung der Variationsprobleme von Lagrange nach Klassen, Comment. Math. Helv. 5 (1933), no. 1, 1–19 (German). MR 1509462, DOI 10.1007/BF01297501 Hestenes, Sufficient conditions for the problem of Bolza in the calculus of variations, these Transactions, vol. 35 (1934).
- A. E. Currier, The variable end point problem of the calculus of variations including a generalization of the classical Jacobi conditions, Trans. Amer. Math. Soc. 34 (1932), no. 3, 689–704. MR 1501657, DOI 10.1090/S0002-9947-1932-1501657-6 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.
- Marston Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Ann. of Math. (2) 32 (1931), no. 3, 567–577. MR 1503017, DOI 10.2307/1968252 Morse, Sufficient conditions in the problem of Lagrange with variable end points, American Journal of Mathematics, vol. 53 (1931), pp. 517-546. 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.
Additional Information
- © Copyright 1935 American Mathematical Society
- 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