Skip to main content
SpringerLink
Log in

Analytic expansion of periodic solutions of integro-differential systems

  • Integral Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We constructively obtain conditions for the existence of periodic solutions of systems of integro-differential equations in the degenerate case. By using integro-differential equations with a parameter, we construct an analytic representation of the solutions and obtain estimates for the convergence rate of iterative processes and for the exact solutions.

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. Bykov, Ya.V., Periodicheskie resheniya differentsial’nykh i integro-differentsial’nykh uravnenii i ikh asimptotiki (Periodic Solutions of Differential and Integro-Differential Equations and Their Asymptotics), Frunze: Ilim, 1986.

    Google Scholar 

  2. Samoilenko, A.M. and Nurzhanov, O.D., The Galerkin-BubnovMethod for the Construction of Solutions of Volterra Type Integro-Differential Equations, Differ. Uravn., 1979, vol. 15, no. 8, pp. 1503–1517.

    MathSciNet  Google Scholar 

  3. Samoilenko, A.M. and Ronto, N.I., Chislenno-analiticheskie metody issledovaniya periodicheskikh reshenii (Numerical-Analytic Methods for the Study of Periodic Solutions), Kiev: Vyshcha Shkola, 1976.

    Google Scholar 

  4. Bakhabov, G.M., A Numerical-Analytic Method of Investigation of Periodic Systems of Integro-Differential Equations, Ukrain. Mat. Zh., 1969, vol. 21, no. 5, pp. 675–683.

    MATH  Google Scholar 

  5. Perestyuk, N.A., Sarafova, M.N., and Khekimov, M.A., Periodic Solutions of Weakly Nonlinear Integro-Differential Equations with Impulsive Action, Vestnik Kiev. Univ., 1980, no. 22, pp. 96–101.

  6. Laptinskii, V.N. and Podolyan, S.V., On an Approximate Solution of a Fredholm Integral Equation of the Second Kind, Deposited in VINITI, Mogilev, 1979, no. 706.

  7. Samoilenko, A.M., Laptinskii, V.N., and Kenzhebaev, K.K., Konstruktivnye metody issledovaniya periodicheskikh i mnogotochechnykh kraevykh zadach (Constructive Methods for the Analysis of Periodic and Many-Point Boundary Value Problems), Kiev: Inst. Mat., 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kirovograd State Pedagogical University, Kirovograd, Ukraine

    G. V. Zavizion

Authors
  1. G. V. Zavizion
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © G.V. Zavizion, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 2, pp. 234–242.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zavizion, G.V. Analytic expansion of periodic solutions of integro-differential systems. Diff Equat 45, 240–248 (2009). https://doi.org/10.1134/S0012266109020104

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266109020104

Keywords

Search

Navigation