Journal of Mathematical Sciences

, Volume 70, Issue 1, pp 1513–1523 | Cite as

The inverse problem for variational computation and its application to the integration of nonlinear ordinary differential equations of higher order

  • M. M. Kabal'skii
Numerical Methods and the Solution of Equations


A method is established for constructing a functional of the variational problem associated with a given nonlinear differential equation of higher order. The Cauchy problem for strongly nonlinear differential equations is solved. The application of this method to the solution of the problem of the resistance of materials is examined.


Differential Equation Ordinary Differential Equation Inverse Problem Cauchy Problem Variational Problem 
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  1. 1.
    G. S. Pisarenko, V. A. Agarev, A. L. Kvitka, et al., Resistance of Materials [in Russian], Vishcha Shkola Golovnoe Izd., Kiev, 1986.Google Scholar
  2. 2.
    V. I. Smirnov, V. I. Krylov, and L. V. Kantorovich, The Variational Calculus [in Russian], KUBUCH, Leningrad, 1933.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • M. M. Kabal'skii
    • 1
  1. 1.Kiev

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