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Normality and abnormality in the calculus of variations. (English) Zbl 0019.12303

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[1] Bolza, Vorlesungen über Variationsrechnung, 1st edition, 1909; 2d edition, 1933. · JFM 40.0428.01
[2] Gilbert Ames Bliss, The Problem of Lagrange in the Calculus of Variations, Amer. J. Math. 52 (1930), no. 4, 673 – 744. · JFM 56.0435.01
[3] Marston Morse, Sufficient Conditions in the Problem of Lagrange with Variable End Conditions, Amer. J. Math. 53 (1931), no. 3, 517 – 546. · Zbl 0002.14101
[4] Marston Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Ann. of Math. (2) 32 (1931), no. 3, 567 – 577. · Zbl 0002.14002
[5] Gilbert Ames Bliss, The problem of Bolza in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 2, 261 – 274. · Zbl 0004.15502
[6] Carathéodory, Die Theorie der zweiten Variation beim Problem von Lagrange, Sitzungsberichte der Bayerischen Akademie der Wissenschaften, 1932, pp. 99-114. · JFM 58.0534.03
[7] Carathéodory, Über die Einteilung der Lagrangeschen Variationsprobleme nach Klassen, Commentarii Mathematici Helvetici, vol. 5 (1933), pp. 1-10. · Zbl 0006.06004
[8] 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. · Zbl 0005.29803
[9] 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. · Zbl 0006.25903
[10] Hestenes, Sufficient conditions for the general problem of Mayer with variable end points, these Transactions, vol. 35 (1933), pp. 479-490; also Contributions to the Calculus of Variations 1931-1932, The University of Chicago. · Zbl 0006.35001
[11] 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. · Zbl 0010.30602
[12] Bliss, The problem of Bolza, Mimeographed lecture notes, University of Chicago, Winter Quarter, 1935.
[13] Marston Morse, Sufficient conditions in the problem of Lagrange without assumptions of normalcy, Trans. Amer. Math. Soc. 37 (1935), no. 1, 147 – 160. · Zbl 0011.02801
[14] Magnus R. Hestenes, The Problem of Bolza in the Calculus of Variations in Parametric Form, Amer. J. Math. 58 (1936), no. 2, 391 – 406. · Zbl 0014.11803
[15] 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. · Zbl 0012.26001
[16] Magnus R. Hestenes, On sufficient conditions in the problems of Lagrange and Bolza, Ann. of Math. (2) 37 (1936), no. 3, 543 – 551. · Zbl 0015.02603
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