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The existence of solutions to classical variational problems without assuming convexity. (English) Zbl 0239.49001


MSC:

49J10 Existence theories for free problems in two or more independent variables
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[1] L. È. Èl\(^{\prime}\)sgol\(^{\prime}\)c, Calculus of variations, Pergamon Press Ltd., London-Paris-Frankfurt, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962.
[2] C. Carathéodory, Calculus of variations and partial differential equations of the first order. Part II: Calculus of variations, Translated from the German by Robert B. Dean, Julius J. Brandstatter, translating editor, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1967. · Zbl 0152.31602
[3] O. Bolza, Vorlesungen über Variationsrechnung, Teubner, Leipzig and Berlin, 1909, Chap. 9. · JFM 40.0428.01
[4] L. C. Young, Lectures on the calculus of variations and optimal control theory, Foreword by Wendell H. Fleming, W. B. Saunders Co., Philadelphia-London-Toronto, Ont., 1969. · Zbl 0177.37801
[5] Calculus of variations, classical and modern, 1 Ciclo, Bressanone 10-18 giugno, vol. 1966, Edizioni Cremonese, Rome, 1967.
[6] C. Carathéodory, Über die starken maxima und minima bei einfachen Integralen, Math. Ann. 62 (1906), no. 4, 449 – 503 (German). · JFM 37.0396.01
[7] Lawrence M. Graves, Discontinuous Solutions in Space Problems of the Calculus of Variations, Amer. J. Math. 52 (1930), no. 1, 1 – 28. · JFM 56.0432.04
[8] L. M. Graves, Discontinuous solutions in the calculus of variations, Bull. Amer. Math. Soc. 36 (1930), 831-846. · JFM 56.0432.03
[9] L. Tonelli, Sull’esistenza del minimo in problemi di calcolo delle variazioni, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 1 (1931), 89-100. · Zbl 0003.16101
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