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

A direct sufficiency proof for the problem of Bolza in the calculus of variations
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Trans. Amer. Math. Soc. 42 (1937), 141-154

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

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References

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Sufficient conditions in the problem of Lagrange with variable end points

Gilbert Ames Bliss, The problem of Bolza in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 2, 261–274. MR 1503050, DOI 10.2307/1968328
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, DOI 10.1090/S0002-9947-1934-1501767-5
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, DOI 10.1090/S0002-9947-1935-1501780-9
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, DOI 10.2307/2371189

The problem of Bolza in the calculus of variations

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, DOI 10.2307/1968477

Sufficient conditions by expansion methods for the problem of Bolza in the calculus of variations in parametric form