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Boundary-value problems for integral equations with degenerate kernel

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We consider boundary-value problems for integral equations with degenerate kernel. Using a pseudoinverse operator, we establish conditions for the existence of a unique solution of the original integral equation and obtain a representation for this solution. We also establish conditions for the existence of a solution of a boundary-value problem for this equation and obtain a representation of this solution. The results are illustrated by examples.

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References

  1. S. G. Krein, Linear Equations in a Banach Space [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  2. A. A. Boichuk, Constructive Methods for Analysis of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  3. A. A. Boichuk and V. F. Zhuravlev, “Construction of solutions of boundary-value problems for differential systems with delay in critical cases,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 6, 3–6 (1990).

  4. A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1995).

    Google Scholar 

  5. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  6. A. M. Samoilenko, A. A. Boichuk, and S. A. Krivosheya, “Boundary-value problem for linear systems of integro-differential equations with degenerate kernel,” Ukr. Mat. Zh., 48, No. 11, 1576–1579 (1996); English translation: Ukr. Math. J., 48, No. 11, 1785–1789 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, VSP, Utrecht (2004).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Zhytomyr National Agroecological University, Zhytomyr, Ukraine

    V. F. Zhuravlev

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  1. V. F. Zhuravlev
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Correspondence to V. F. Zhuravlev.

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Translated from Neliniini Kolyvannya, Vol. 15, No. 1, pp. 36–54, January–March, 2012.

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Zhuravlev, V.F. Boundary-value problems for integral equations with degenerate kernel. J Math Sci 187, 413–431 (2012). https://doi.org/10.1007/s10958-012-1073-z

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  • DOI: https://doi.org/10.1007/s10958-012-1073-z

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