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On a Class of Systems of Linear and Nonlinear Fredholm Integral Equations of the Third Kind with Multipoint Singularities

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Abstract

Based on a new approach, we show that finding solutions for a class of systems of linear (respectively, nonlinear) Fredholm integral equations of the third kind with multipoint singularities is equivalent to finding solutions of systems of linear (respectively, nonlinear) Fredholm integral equations of the second kind with additional conditions. We study the existence, nonexistence, uniqueness, and nonuniqueness of solutions for this class of systems of Fredholm integral equations of the third kind with multipoint singularities.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of the Kyrgyz Republic, Bishkek, 720071, Kyrgyzstan

    M. I. Imanaliev

  2. Kyrgyz Turkish Manas University, Bishkek, 720044, Kyrgyzstan

    A. Asanov

  3. Razzakov Kyrgyz State Technical University, Bishkek, 720044, Kyrgyzstan

    R. A. Asanov

Authors
  1. M. I. Imanaliev
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  2. A. Asanov
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  3. R. A. Asanov
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Additional information

Original Russian Text © M.I. Imanaliev, A. Asanov, R.A. Asanov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 3, pp. 387–397.

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Imanaliev, M.I., Asanov, A. & Asanov, R.A. On a Class of Systems of Linear and Nonlinear Fredholm Integral Equations of the Third Kind with Multipoint Singularities. Diff Equat 54, 381–391 (2018). https://doi.org/10.1134/S0012266118030096

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  • DOI: https://doi.org/10.1134/S0012266118030096

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