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Lobachevskii Journal of Mathematics

ISSN
1818-9962
1995-0802
Издатель
Pleiades Publishing
Ключевые слова

Differential Equation...

Nonlinear Differentia...

Holomorphic and Opera...

Probability and Stati...

Spectral Theory in Ma...

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    Тип записи:Публикация,
    On the Unique Solvability of a Family of Boundary Value Problems for Integro-Differential Equations of Mixed Type
    (Pleiades Publishing, 2021-06-01)
    A. T. Assanova
    ;
    A. P. Sabalakhova
    ;
    Z. M. Toleukhanova
    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.
    Цитирования (OpenAlex) 6Цитирования (OpenCitations) 5