Skip to main content
SpringerLink
Log in

Inverse problem of the variational calculus for differential equations of second order with deviating argument

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We obtain conditions for the solvability of the inverse problem of the variational calculus for differential equations of second order with deviating argument of special form as well as the formula for the functional of the inverse problem defined by the integral that differs from the standard one by that the required function has a retarded argument.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. G. Zadorozhnii, Methods of Variational Analysis (IKI, Moscow-Izhevsk, 2006) [in Russian].

    Google Scholar 

  2. L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument (Nauka, Moscow, 1971) [in Russian].

    MATH  Google Scholar 

  3. L. É. Él’sgol’ts, Qualitative Methods in Mathematical Analysis (Gostekhizdat, Moscow, 1955) [in Russian].

    Google Scholar 

  4. G. Kamenskii, “On boundary value problems connected with variational problems for nonlocal functionals,” Funct. Differ. Equ. 12(3–4), 245–270 (2005).

    MathSciNet  Google Scholar 

  5. G. A. Kamenskii, “Asymmetrical variational problems for functionals with deviating argument,” Ukrain.Mat. Zh. 41(5), 602–609 (1989) [UkrainianMath. J. 41 (5), 521–527 (1989)].

    MathSciNet  Google Scholar 

  6. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, 3d ed. (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  7. L. S. Gnoenskii, G. A. Kamenskii, and L. É. Él’sgol’ts, Mathematical Foundations of the Theory of Control Systems (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    V. G. Zadorozhnii

  2. Voronezh State Academy of Forestry Engineering, Voronezh, Russia

    G. A. Kurina

Authors
  1. V. G. Zadorozhnii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. A. Kurina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Zadorozhnii.

Additional information

Original Russian Text © V. G. Zadorozhnii, G. A. Kurina, 2011, published in Matematicheskie Zametki, 2011, Vol. 90, No. 2, pp. 231–241.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zadorozhnii, V.G., Kurina, G.A. Inverse problem of the variational calculus for differential equations of second order with deviating argument. Math Notes 90, 218 (2011). https://doi.org/10.1134/S0001434611070212

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1134/S0001434611070212

Keywords

Search

Navigation