Abstract
We study the extremals of problems of the classical calculus of variations. We obtain a new necessary condition for a strong minimum under the assumption that the Weierstrass and Legendre conditions degenerate, i.e., are satisfied as equalities, on the extremal under study; this condition is called a generalized Weierstrass condition. We also give a modified condition that is a necessary condition for a weak minimum.
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Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extremal Problems), Moscow: Nauka, 1974.
Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., Optimal’noe upravlenie (Optimal Control), Moscow: Nauka, 2007.
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Russian Text © A.V. Arutyunov, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 1, pp. 74–82.
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Arutyunov, A.V. Generalized Weierstrass Condition in the Classical Calculus of Variations. Diff Equat 55, 75–83 (2019). https://doi.org/10.1134/S0012266119010087
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DOI: https://doi.org/10.1134/S0012266119010087