Skip to main content
SpringerLink
Log in

Integro-Differential Equation of the Convolution Type with a Power Nonlinearity and an Inhomogeneity in the Linear Part

  • INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

For an integro-differential equation of the convolution type defined on the half-line \([0,\infty ) \) with a power nonlinearity and an inhomogeneity in the linear part, we use the weight metrics method to prove a global theorem on the existence and uniqueness of a solution in the cone of nonnegative functions in the space \(C[0,\infty ) \). It is shown that the solution can be found by a successive approximation method of the Picard type; an estimate for the rate of convergence of the approximations is produced.

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. Okrasinski, W., Nonlinear Volterra equations and physical applications,Extracta Math., 1989, vol. 4, no. 2, pp. 51–74.

    MathSciNet  Google Scholar 

  2. Askhabov, S.N., Integral equations of convolution type with power nonlinearity, Colloq. Math., 1991, vol. 62, no. 1, pp. 49–65.

    Article  MathSciNet  Google Scholar 

  3. Askhabov, S.N., Nelineinye uravneniya tipa svertki (Nonlinear Equations of Convolution Type), Moscow: Fizmatlit, 2009.

    Google Scholar 

  4. Brunner, H., Volterra Integral Equations: an Introduction to the Theory and Applications, Cambridge: Cambridge Univ. Press, 2017.

    Book  Google Scholar 

  5. Edwards, R.E., Functional Analysis: Theory and Applications, New York: Holt, Rinehart, and Winston, 1965. Translated under the title: Funktsional’nyi analiz, Moscow: Mir, 1969.

    MATH  Google Scholar 

  6. Okrasinski, W., On a nonlinear Volterra equation, Math. Meth. Appl. Sci., 1986, vol. 8, no. 3, pp. 345–350.

    MathSciNet  MATH  Google Scholar 

  7. Okrasinski, W., On the existence and uniqueness of nonnegative solutions of a certain nonlinear convolution equation, Annal. Polon. Math., 1979, vol. 36, no. 1, pp. 61–72.

    Article  MathSciNet  Google Scholar 

  8. Askhabov, S.N. and Betilgiriev, M.A., A priori bounds of solutions of the nonlinear integral convolution type equation and their applications, Math. Notes, 1993, vol. 54, no. 5, pp. 1087–1092.

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-41-200001.

Author information

Authors and Affiliations

  1. Chechen State Pedagogical University, Groznyi, 364068, Russia

    S. N. Askhabov

  2. Chechen State University, Groznyi, 364024, Russia

    S. N. Askhabov

Authors
  1. S. N. Askhabov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. N. Askhabov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Askhabov, S.N. Integro-Differential Equation of the Convolution Type with a Power Nonlinearity and an Inhomogeneity in the Linear Part. Diff Equat 56, 775–784 (2020). https://doi.org/10.1134/S0012266120060105

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266120060105

Search

Navigation