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]**William T. Reid,*Isoperimetric problems of Bolza in nonparametric form*, Duke Math. J.**5**(1939), 675–691. MR**0000100****[2]**E. J. McShane,*Sufficient conditions for a weak relative minimum in the problem of Bolza*, Trans. Amer. Math. Soc.**52**(1942), 344–379. MR**0006828**, https://doi.org/10.1090/S0002-9947-1942-0006828-2**[3]**Franklin G. Myers,*Sufficiency conditions for the problem of Lagrange*, Duke Math. J.**10**(1943), 73–97. MR**0007836****[4]**Magnus R. Hestenes,*The Weierstrass 𝐸-function in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 51–71. MR**0017478**, https://doi.org/10.1090/S0002-9947-1946-0017478-X**[5]**Magnus R. Hestenes,*Theorem of Lindeberg in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 72–92. MR**0017479**, https://doi.org/10.1090/S0002-9947-1946-0017479-1**[6]**Magnus R. Hestenes,*Sufficient conditions for the isoperimetric problem of Bolza in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 93–118. MR**0017480**, https://doi.org/10.1090/S0002-9947-1946-0017480-8**[7]**Magnus R. Hestenes,*An alternate sufficiency proof for the normal problem of Bolza*, Trans. Amer. Math. Soc.**61**(1947), 256–264. MR**0020220**, https://doi.org/10.1090/S0002-9947-1947-0020220-0**[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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Additional Information

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

Article copyright:
© Copyright 1947
American Mathematical Society