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On the Unique Solvability of a Family of Boundary Value Problems for Integro-Differential Equations of Mixed Type

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Abstract

The family of boundary value problems for a system of integro-differential equations of mixed type is considered. First, considered problem is reduced to the family of boundary value problems for the Fredholm integro-differential equations with an unknown function and the integral relation. Further, based on the introduction of an additional parameter as a value of the solution at the beginning line of the domain, the problem is reduced to an equivalent problem containing the family of Cauchy problems for the system of Fredholm integro-differential equations with a parameter and the unknown function, and the hybrid system of functional and integral equations for the parameter and the unknown function, respectively. Conditions for the unique solvability of the considered problem are obtained in the terms of the solvability to family of Cauchy problems and the hybrid system.

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Funding

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09258829).

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    A. T. Assanova

  2. M. Auezov South Kazakhstan University, Shymkent, Kazakhstan

    A. P. Sabalakhova

  3. Kazakh National Women’s Teacher Training University, Almaty, Kazakhstan

    Z. M. Toleukhanova

Authors
  1. A. T. Assanova
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  2. A. P. Sabalakhova
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  3. Z. M. Toleukhanova
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Corresponding authors

Correspondence to A. T. Assanova, A. P. Sabalakhova or Z. M. Toleukhanova.

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(Submitted by T. K. Yuldashev)

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Assanova, A.T., Sabalakhova, A.P. & Toleukhanova, Z.M. On the Unique Solvability of a Family of Boundary Value Problems for Integro-Differential Equations of Mixed Type. Lobachevskii J Math 42, 1228–1238 (2021). https://doi.org/10.1134/S1995080221060044

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  • DOI: https://doi.org/10.1134/S1995080221060044

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