A direct sufficiency proof for the problem of Bolza in the calculus of variations

Author:
Magnus R. Hestenes

Journal:
Trans. Amer. Math. Soc. **42** (1937), 141-154

MSC:
Primary 49K05

DOI:
https://doi.org/10.1090/S0002-9947-1937-1501917-3

MathSciNet review:
1501917

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References | Similar Articles | Additional Information

**[I]**Bliss,*The problem of Lagrange in the calculus of variations*, American Journal of Mathematics, vol. 52 (1930), pp. 673-744. MR**1506783****[II]**Morse,*Sufficient conditions in the problem of Lagrange with variable end points*, American Journal of Mathematics, vol. 53 (1931), pp. 517-596.**[III]**Bliss,*The problem of Bolza in the calculus of variations*, Annals of Mathematics, (2), vol. 33 (1932), pp. 261-274. MR**1503050****[IV]**Hestenes,*Sufficient conditions for the problem of Bolza in the calculus of variations*, these Transactions, vol. 36 (1934), pp. 793-818. MR**1501767****[V]**Morse,*Sufficient conditions in the problem of Lagrange without assumptions of normalcy*, these Transactions, vol. 37 (1935), pp. 147-160. MR**1501780****[VI]**Reid,*The theory of the second variation for the non-parametric problem of Bolza*, American Journal of Mathematics, vol. 57 (1935), pp. 573-586. MR**1507097****[VII]**Bliss,*The problem of Bolza in the calculus of variations*, Lectures delivered at the University of Chicago during the Winter Quarter, 1935.**[VIII]**Hestenes,*On sufficient conditions in the problems of Lagrange and Bolza*, Annals of Mathematics, (2), vol. 37 (1936), pp. 543-551. MR**1503298****[IX]**Reid,*Sufficient conditions by expansion methods for the problem of Bolza in the calculus of variations in parametric form*, Bulletin of the American Mathematical Society, vol. 41 (1935), p. 788, abstract 41-11-379.

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DOI:
https://doi.org/10.1090/S0002-9947-1937-1501917-3

Article copyright:
© Copyright 1937
American Mathematical Society