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Inverse problem of the calculus of variation, its application to integration of an ordinary non-linear second order differential equation

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Abstract

Necessary and sufficient conditions for the existence of a functional for a strongly non-linear differential equation of the second order in ordinary derivatives are established. The Cauchy problem is solved. The integration method is illustrated by solving problems of theoretical mechanics, relativity theory, quasilinear oscillations and strength of materials.

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Literature cited

  1. M. M. Kobal'skii, New Methods of Higher Algebra. Two Volumes [in Russian], Kiev (1982). Deposited in VINITI, No. 1140, No. 1141.

  2. N. M. Krylov, “Sur la solution approcheé des problemes...,” Izv. Akad. Nauk SSSR, No. 5, 3–11 (1929).

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  3. I. N. Molchanov, Mechanical Methods for Solving Applied Problems. Differential Equations [in Russian], Naukova Dumka, Kiev (1988).

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    M. M. Kabal'skii

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  1. M. M. Kabal'skii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 413–418, March, 1990.

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Kabal'skii, M.M. Inverse problem of the calculus of variation, its application to integration of an ordinary non-linear second order differential equation. Ukr Math J 42, 367–371 (1990). https://doi.org/10.1007/BF01057027

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  • DOI: https://doi.org/10.1007/BF01057027

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