Differential Equations

, Volume 55, Issue 1, pp 75–83 | Cite as

Generalized Weierstrass Condition in the Classical Calculus of Variations

  • A. V. ArutyunovEmail author
Control Theory


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.Google Scholar
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    Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., Optimal’noe upravlenie (Optimal Control), Moscow: Nauka, 2007.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Peoples’ Friendship University of RussiaMoscowRussia
  3. 3.Derzhavin Tambov State UniversityTambovRussia

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