Skip to main content
SpringerLink
Log in

On the Solvability of the Periodic Boundary-Value Problem for a First-Order Differential Equation Unsolved with Respect to the Derivative

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we obtain solvability conditions for the periodic boundary-value problem for a certain first-order differential equation unsolved with respect to the derivative. These condition were obtained by using the theorem on implicit operators.

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. A. R. Abdullaev and A. B. Burmistrova, Elements of the Theory of Topological Noether Operators [in Russian], Chelyabinsk State Univ., Chelyabinsk (1994).

    MATH  Google Scholar 

  2. R. E. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York–London–Amsterdam (1965).

    MATH  Google Scholar 

  3. Yu. G. Borisovich, V. G. Zvyagin, and Yu. I. Sapronov, “Nonlinear Fredholm mappings and the Leray–Schauder theory,” Usp. Mat. Nauk, 32, No. 4, 3–54 (1977).

    MathSciNet  MATH  Google Scholar 

  4. J. Diblik, “Existence and uniqueness of solutions to an initial boundary-value problem for differential equations partially solved with respect to derivatives,” preprint VINITI (1984), No. 908-84.

  5. V. T. Dmitrienko, “Two-point boundary-value problem for second-order differential equations unsolved with respect to the leading derivative,” in: Approximate Methods in Differential Equations and Their Applications [in Russian], Kuybyshev (1982), pp. 47–58.

  6. M. N. Eliseenko, “On periodic solutions of a certain second-order ordinary differential equation unsolvable with respect to derivatives,” Differ. Equ., 21, No. 9, 1618–1621 (1985).

    MathSciNet  MATH  Google Scholar 

  7. I. Yu. Kolpakov, “On the solvability of quasilinear operator equations,” Vestn. Perm Perm. Tekh. Univ. Ser. Mat. Prikl. Mat., 21–27 (2002).

  8. L. G. Prosenyuk, “Existence and asymptotics of O-solutions to a differential equation unsolved with respect to the derivative,” Ukr. Mat. Zh., 39, No. 6, 796–799 (1987).

    MathSciNet  MATH  Google Scholar 

  9. A. A. Shcheglova, “Newton’s method for degenerate systems of ordinary differential equations,” Sib. Mat. Zh., 39, No. 6, 1428–1434 (1998).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Perm National Research Polytechnic University, Perm, Russia

    I. Yu. Kolpakov

Authors
  1. I. Yu. Kolpakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Yu. Kolpakov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolpakov, I.Y. On the Solvability of the Periodic Boundary-Value Problem for a First-Order Differential Equation Unsolved with Respect to the Derivative. J Math Sci 230, 695–698 (2018). https://doi.org/10.1007/s10958-018-3771-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3771-7

Keywords and phrases

AMS Subject Classification

Search

Navigation