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Nonlocal Direct and Inverse Problems for a Second Order Nonhomogeneous Fredholm Integro-Differential Equation with Two Redefinition Data

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Abstract

The questions of solvability and construction of solutions of a nonlocal direct and inverse problems for a second-order nonhomogeneous Fredholm integro-differential equation with a degenerate kernel, two redefinition data and two real parameters are considered. The degenerate kernel method is used. The features that have arisen in the construction of solutions and are associated with the determination of the integration coefficients and redefinition data are studied. The values of the parameters are calculated for which the solvability of direct nonlocal problem is established and the corresponding solutions are constructed. It is studied the case when inverse problem has a unique solution.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Osh State University, 723500, Osh, Kyrgyzstan

    Zh. A. Artykova

  2. Azerbaijan University of Architecture and Construction, AZ1073, Baku, Azerbaijan

    R. A. Bandaliyev

  3. Tashkent State University of Economics, 100066, Tashkent, Uzbekistan

    T. K. Yuldashev

Authors
  1. Zh. A. Artykova
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  2. R. A. Bandaliyev
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  3. T. K. Yuldashev
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Correspondence to Zh. A. Artykova, R. A. Bandaliyev or T. K. Yuldashev.

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Artykova, Z.A., Bandaliyev, R.A. & Yuldashev, T.K. Nonlocal Direct and Inverse Problems for a Second Order Nonhomogeneous Fredholm Integro-Differential Equation with Two Redefinition Data. Lobachevskii J Math 44, 4215–4230 (2023). https://doi.org/10.1134/S1995080223100050

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