An indirect sufficiency proof for the problem of Bolza in nonparametric form

Author:
Magnus R. Hestenes

Journal:
Trans. Amer. Math. Soc. **62** (1947), 509-535

MSC:
Primary 49.0X

DOI:
https://doi.org/10.1090/S0002-9947-1947-0023465-9

MathSciNet review:
0023465

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References | Similar Articles | Additional Information

**[1]**W. T. Reid,*Isoperimetric problems of Bolza in nonparametric form*, Duke Math. J. vol. 5 (1939) pp. 675-691. MR**0000100 (1:19b)****[2]**E. J. McShane,*Sufficient conditions for a weak relative minimum in the problem of Bolza*, Trans. Amer. Math. Soc. vol. 52 (1942) pp. 344-379. MR**0006828 (4:48d)****[3]**F. G. Myers,*Sufficient conditions for the problem of Lagrange*, Duke Math. J. vol. 10 (1943) pp. 73-97. MR**0007836 (4:200c)****[4]**M. R. Hestenes,*The Weirstrass -function in the calculus of variations*, Trans. Amer. Math. Soc. vol. 60 (1946) pp. 51-71. MR**0017478 (8:160b)****[5]**-,*The theorem of Lindeberg in the calculus of variations*, Trans. Amer. Math. Soc. vol. 60 (1946) pp. 72-92. MR**0017479 (8:160c)****[6]**-,*Sufficient conditions for the isoperimetric problem of Bolza in the calculus of variations*, Trans. Amer. Math. Soc. vol. 60 (1946) pp. 93-118. MR**0017480 (8:160d)****[7]**-,*An alternate sufficiency proof for the normal problem of Bolza*, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 256-264. MR**0020220 (8:521b)****[8]**A. L. Lewis,*Sufficiency proofs for the problem of Bolza in the calculus of variations*, Dissertation, The University of Chicago, 1943.

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DOI:
https://doi.org/10.1090/S0002-9947-1947-0023465-9

Article copyright:
© Copyright 1947
American Mathematical Society