Skip to main content
SpringerLink
Log in

Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length

  • Research Articles
  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The paper deals with the second boundary-value problem for a second-order differential-difference equation with variable coefficients on the interval \((0,d)\) as well as with the question of conditions on the right-hand side of the equation that ensure the smoothness of the generalized solutions of the boundary-value problem on the whole interval \((0,d)\) for \(d \notin \mathbb{N}\).

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. Yu. S. Osipov, “On stabilization of control systems with delay,” Differ. Uravn. 1 (5), 605–618 (1965).

    MathSciNet  MATH  Google Scholar 

  2. N. N. Krasovskii, Theory of Control of Motion: Linear Systems (Nauka, Moscow, 1968) [in Russian].

    MATH  Google Scholar 

  3. A. V. Kryazhimskii, V. I. Maksimov, and Yu. S. Osipov, “On positional simulation in dynamic systems,” J. Appl. Math. Mech. 47 (6), 709–714 (1985).

    Article  MathSciNet  Google Scholar 

  4. A. L. Skubachevskii, “On the problem of damping a control system with aftereffect,” Dokl. Math. 49 (2), 282–286 (1994).

    Article  MathSciNet  Google Scholar 

  5. A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications (Birkhäuser, Basel, 1997).

    MATH  Google Scholar 

  6. G. A. Kamenskii and A. D. Myshkis, “On the formulation of boundary value problems for differential equations with deviating argument and several highest terms,” Differ. Uravn. 10 (3), 409–418 (1974).

    MathSciNet  Google Scholar 

  7. A. G. Kamenskii, “Boundary value problems for equations with formally symmetric differential-difference operators,” Differ. Uravn. 12 (5), 815–824 (1976).

    MathSciNet  Google Scholar 

  8. D. A. Neverova and A. L. Skubachevskii, “On the classical and generalized solutions of boundary-value problems for difference-differential equations with variable coefficients,” Math. Notes 94 (5), 653–667 (2013).

    Article  MathSciNet  Google Scholar 

  9. D. A. Neverova, “Generalized and classical solutions to the second and third boundary-value problem for differential-difference equations,” Funct. Differ. Equ. 21 (1-2), 47–65 (2014).

    MathSciNet  MATH  Google Scholar 

  10. G. A. Kamenskii, A. D. Myshkis, and A. L. Skubachevskii, “Smooth solutions of a boundary value problem for a differential-difference equation of neutral type,” Ukrain. Mat. Zh. 37 (5), 581–589 (1985).

    MathSciNet  MATH  Google Scholar 

  11. V. V. Liiko and A. L. Skubachevskii, “Mixed problems for strongly elliptic differential-difference equations in a cylinder,” Math. Notes 107 (5), 770–790 (2020).

    Article  MathSciNet  Google Scholar 

  12. A. L. Skubachevskii and N. O. Ivanov, “On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients,” in CMFD, Dedicated to 70th anniversary of the President of RUDN University V. M. Filippov (PFUR, Moscow, 2021), Vol. 67, pp. 576–595.

    MathSciNet  Google Scholar 

  13. A. L. Skubachevskii and N. O. Ivanov, “The second boundary-value problem for differential-difference equations,” Dokl. Akad. Nauk 500 (1), 74–77 (2021).

    MATH  Google Scholar 

Download references

Acknowledgments

The authors wish to express gratitude to L. E. Rossovsky for a number of suggestions that led to the improvement of the paper.

Funding

The work of the first author was supported by the Russian Foundation for Basic Research under grant no. 20-01-00288.

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198, Russia

    A. L. Skubachevskii & N. O. Ivanov

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    A. L. Skubachevskii

Authors
  1. A. L. Skubachevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. O. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. L. Skubachevskii.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 873–886 https://doi.org/10.4213/mzm13439.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Skubachevskii, A.L., Ivanov, N.O. Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length. Math Notes 111, 913–924 (2022). https://doi.org/10.1134/S000143462205025X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000143462205025X

Keywords

Search

Navigation