References
Bakhvalov N. S., Numerical Methods [in Russian], Nauka, Moscow (1975).
Tonelli L., Fondamenti di Calcolo delle Variazioni. Vol. 2, Zanichelli, Bologna (1923).
Bernsteîn S. N., Collected Works. Vol. 3 [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1960).
Clarke F. H. andVinter R. B., “Regularity properties of solutions to the basic problem in the calculus of variations,” Trans. Amer. Math. Soc.,289, No. 1, 74–98 (1985).
Davi A. M., “Singular minimisers in the calculus of variations in one dimension,” Arch. Rational Mech. Anal.,101, No. 2, 161–177 (1988).
Lavrentiev M., “Sur quelques problems du calcul des variations,” Ann. Mat. Pura Appl. (4),4, 7–28 (1926).
Belonosov V. S. andZelenyak T. I., Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Novosibirsk Univ., Novosibirsk (1975).
Natanson I. P., Theory of Functions of a Real Variable [in Russian], Gostekhizdat., Moscow (1950).
Kosha A., Variational Calculus [Russian translation], Vysshaya Shkola, Moscow (1983).
Zelenyak T. I. andLyul’ko N. A., “To the question of global solvability of mixed problems for quasilinear parabolic equations,” Sibirsk. Mat. Zh.,39, No. 2, 317–328 (1998).
Akramov T. A. andZelenyak T. I., “On the number of stationary solutions and instability domains for quasilinear parabolic equations,” in: Mathematical Problems of Chemistry. I [in Russian], Inst. Kataliza Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk, 1975, pp. 144–150.
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 5, pp. 1060–1075, September–October, 2000.
Rights and permissions
About this article
Cite this article
Zelenyak, T.I., Lyul’ko, N.A. On a method for solving a classical variational problem. Sib Math J 41, 866–879 (2000). https://doi.org/10.1007/BF02674742
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674742