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

MathSciNet review:
1501917

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References | Similar Articles | Additional Information

**[I]**Gilbert Ames Bliss,*The Problem of Lagrange in the Calculus of Variations*, Amer. J. Math.**52**(1930), no. 4, 673–744. MR**1506783**, 10.2307/2370714**[II]**Morse,*Sufficient conditions in the problem of Lagrange with variable end points*, American Journal of Mathematics, vol. 53 (1931), pp. 517-596.**[III]**Gilbert Ames Bliss,*The problem of Bolza in the calculus of variations*, Ann. of Math. (2)**33**(1932), no. 2, 261–274. MR**1503050**, 10.2307/1968328**[IV]**Magnus R. Hestenes,*Sufficient conditions for the problem of Bolza in the calculus of variations*, Trans. Amer. Math. Soc.**36**(1934), no. 4, 793–818. MR**1501767**, 10.1090/S0002-9947-1934-1501767-5**[V]**Marston Morse,*Sufficient conditions in the problem of Lagrange without assumptions of normalcy*, Trans. Amer. Math. Soc.**37**(1935), no. 1, 147–160. MR**1501780**, 10.1090/S0002-9947-1935-1501780-9**[VI]**William T. Reid,*The Theory of the Second Variation for the Non-Parametric Problem of Bolza*, Amer. J. Math.**57**(1935), no. 3, 573–586. MR**1507097**, 10.2307/2371189**[VII]**Bliss,*The problem of Bolza in the calculus of variations*, Lectures delivered at the University of Chicago during the Winter Quarter, 1935.**[VIII]**Magnus R. Hestenes,*On sufficient conditions in the problems of Lagrange and Bolza*, Ann. of Math. (2)**37**(1936), no. 3, 543–551. MR**1503298**, 10.2307/1968477**[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:
http://dx.doi.org/10.1090/S0002-9947-1937-1501917-3

Article copyright:
© Copyright 1937
American Mathematical Society