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Volterra functional integral equation of the first kind with nonlinear right-hand side and variable limits of integration

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Abstract

We prove a theorem on the existence and uniqueness of a solution of a Volterra functional integral equation of the first kind with nonlinear right-hand side and nonlinear deviation. We use the method of successive approximations combined with the method of contracting mappings.

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References

  1. A. Asanov, “Stability of solutions of systems of linear Volterra integral equations of the second kind on a half interval,” Issled. Integro-Differents. Uravn., Issue 22, 123–129 (1989).

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  2. T. K. Yuldashev and J. A. Artykova, “Volterra integral equation of the first kind with nonlinear right-hand side,” Sklad. Syst. Prots., Nos. 1, 2, 3–5 (2005).

  3. T. K. Yuldashev and J. A. Artykova, “Random Volterra integral equations of the first kind with nonlinear right-hand side,” in: Proceedings of the Fifth International Fergana Conference “Limit Theorems in Probability Theory and Their Applications” (Fergana, May 10–12, 2005), Institute of Mathematics, Uzbek Academy of Sciences, Tashkent (2005), pp. 204–206.

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  4. T. K. Yuldashev and J. A. Artykova, “Volterra integral equation of the first kind with nonlinear right-hand side and compound deviation,” Abstracts of the International Seminar “Geometry in Odessa-2005. Differential Geometry and Its Applications (Odessa, May 23–29, 2005), Odessa (2005), pp. 112–113.

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Authors and Affiliations

  1. Kyrgyz State Law Academy, Osh, Kyrgyzstan

    T. K. Yuldashev

  2. Osh University, Kyrgyzstan

    J. A. Artykova

Authors
  1. T. K. Yuldashev
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  2. J. A. Artykova
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1285–1288, September, 2006.

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Yuldashev, T.K., Artykova, J.A. Volterra functional integral equation of the first kind with nonlinear right-hand side and variable limits of integration. Ukr Math J 58, 1458–1461 (2006). https://doi.org/10.1007/s11253-006-0145-y

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  • DOI: https://doi.org/10.1007/s11253-006-0145-y

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