Skip to main content
Log in

Generalizaed Solutions to the Cauchy Problem for the Barbashin Integro-differential Equations

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

We establish the existence and uniqueness of a generalized solution to the Cauchy problem for the Barbashin integro-differential equation and a system of such equations. The results are illustrated by examples. Bibliography: 6 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. M. Appell, A. S. Kalitvin, and P. P. Zabrejko, Partial Integral Operators and Integro-Differential Equations, Marcel Dekker, New York (2000).

    MATH  Google Scholar 

  2. G. Brack, “Systems with substantially distributed parameters,” Math. Res. 27, 421–424 (1985).

    MathSciNet  Google Scholar 

  3. A. S. Kalitvin, “Some aspects of the theory of integro-differential Barbashin equations in function spaces” [in Russian], Probl. Mat. Anal. 67, 61–68 (2012); J. Math. Sci., New York 188, No. 3, 241–249 (2013).

  4. A. S. Kalitvin and V. A. Kalitvin, Volterra and Volterra–Fredholm Integral Equations with Partial Integrals [in Russian], Lipetsk (2006).

  5. V. L. Levin, “Tensor products and functors in categories of Banach spaces defined by KM-lineals” [in Russian], Tr. Moskov. Mat. Ob-va 20, 43–82 (1969); English transl.: Trans. Mosc. Math. Soc. 20, 41–77 (1969).

  6. N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, John Wiley & Sons, New York etc. (1988)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. S. Kalitvin.

Additional information

Translated from Problemy Matematicheskogo Analiza 80, April 2015, pp. 11-17.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalitvin, A.S. Generalizaed Solutions to the Cauchy Problem for the Barbashin Integro-differential Equations. J Math Sci 208, 160–167 (2015). https://doi.org/10.1007/s10958-015-2433-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2433-2

Keywords

Navigation