Skip to main content
SpringerLink
Log in

Averaging of initial-value and boundary-value problems for one class of oscillatory impulsive systems

  • Published:
Nonlinear Oscillations

Abstract

We give a new classification of fixed times of pulse action (uniform, functional, limiting, and quantitatively limiting). Several results obtained earlier for oscillatory systems with uniform and limiting times of pulse action are generalized to similar systems with functional times of pulse action. Namely, we obtain estimates, which are exact with respect to a small parameter ε, for the deviation of solutions and their partial derivatives for original and averaged initial-value, boundary-value, and multipoint problems.

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. M. Samoilenko and R. I. Petryshyn, Mathematical Aspects of the Theory of Nonlinear Oscillations [in Ukrainian], Naukova Dumka, Kyiv (2004).

    Google Scholar 

  2. A. M. Samoilenko, “On the problem of justification of averaging method for multifrequency oscillatory systems,” Differents. Uravn., 23, No. 2, 267–278 (1987).

    Google Scholar 

  3. A. M. Samoilenko, “Averaging method in systems with pulses,” Mat. Fiz., 9, 101–117 (1971).

    Google Scholar 

  4. R. I. Petryshyn and T. M. Sopronyuk, “Justification of averaging method for multifrequency impulsive systems,” Ukr. Mat. Zh., 55, No. 1, 55–65 (2003).

    Article  MATH  Google Scholar 

  5. T. M. Sopronyuk, Oscillations of Multifrequency Impulsive Systems [in Ukrainian], Candidate-Degree Thesis (Physics and Mathematics), Kyiv (2003).

  6. T. M. Sopronyuk, “Asymptotic stability of solutions of a nonlinear impulsive system with small parameter,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 111, 113–120 (2001).

  7. Ya. R. Petryshyn, “Justification of averaging method on a semiaxis for one class of nonlinear oscillatory systems with pulse action,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 111, 105–109 (2001).

  8. R. I. Petryshyn and T. M. Sopronyuk, “Averaging of a boundary-value problem with integral boundary conditions and parameters for a multifrequency impulsive system,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 228, 96–107 (2004).

  9. T. M. Sopronyuk and P. M. Dudnyts’kyi, “Multipoint problem with parameters for a multifrequency impulsive system,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 191/192, 128–136 (2004).

  10. T. M. Sopronyuk, “Averaging of oscillatory impulsive systems on a segment,” in: Abstracts of the International Conference “Differential Equations and Their Applications,” Shevchenko Kyiv National University, Kyiv (2005), p. 103.

    Google Scholar 

  11. R. I. Petryshyn and P. M. Dudnyts’kyi, “Averaging of multifrequency systems with nonfixed times of pulse action,” in: Abstracts of the International Conference “Differential Equations and Their Applications,” Shevchenko Kyiv National University, Kyiv (2005), p. 84.

    Google Scholar 

  12. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chernivtsi National University, Chernivtsi

    R. I. Petryshyn & T. M. Sopronyuk

Authors
  1. R. I. Petryshyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. M. Sopronyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 68–84, January–March, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petryshyn, R.I., Sopronyuk, T.M. Averaging of initial-value and boundary-value problems for one class of oscillatory impulsive systems. Nonlinear Oscill 9, 65–82 (2006). https://doi.org/10.1007/s11072-006-0026-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11072-006-0026-1

Keywords

Search

Navigation