Normality and abnormality in the calculus of variations

Normality and abnormality in the calculus of variations
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by G. A. Bliss

Trans. Amer. Math. Soc. 43 (1938), 365-376

DOI: https://doi.org/10.1090/S0002-9947-1938-1501950-2

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References

Vorlesungen über Variationsrechnung

Gilbert Ames Bliss, The Problem of Lagrange in the Calculus of Variations, Amer. J. Math. 52 (1930), no. 4, 673–744. MR 1506783, DOI 10.2307/2370714
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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

Die Theorie der zweiten Variation beim Problem von Lagrange

Über die Einteilung der Lagrangeschen Variationsprobleme nach Klassen

Lawrence M. Graves, On the Weierstrass condition for the problem of Bolza in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 4, 747–752. MR 1503088, DOI 10.2307/1968217
G. A. Bliss and M. R. Hestenes, Sufficient conditions for a problem of Mayer in the calculus of variations, Trans. Amer. Math. Soc. 35 (1933), no. 1, 305–326. MR 1501685, DOI 10.1090/S0002-9947-1933-1501685-1

Sufficient conditions for the general problem of Mayer with variable end points

Contributions to the Calculus of Variations

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

The problem of Bolza

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
Magnus R. Hestenes, The Problem of Bolza in the Calculus of Variations in Parametric Form, Amer. J. Math. 58 (1936), no. 2, 391–406. MR 1507162, DOI 10.2307/2371048
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
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