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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References | Similar Articles | Additional Information

**[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 as against the author's weaker assumption that a 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