On the Unique Solvability of a Boundary Value Problem for Systems of Loaded Integro-Differential Equations with Involution
Usmanov K.I. Nazarova K.Z. Yerkisheva Z.S.
December 2021Pleiades journals
Lobachevskii Journal of Mathematics
2021#42Issue 123022 - 3034 pp.
Abstract: In this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory transformation. The parameterization method is applied to the boundary value problem for a system with continuous kernel. By using the properties of involutory transformation, the problem is transformed to a boundary value problem for systems of loaded integro-differential equations. The latter problem, in turn, is reduced to solving a special Cauchy problem and a system of algebraic equations in parameters introduced. An algorithm for solving the boundary value problem for systems of loaded integro-differential equations is proposed. On the basis of this algorithm, necessary conditions for the unique solvability of the original problem are established. We also consider a boundary value problem for a systems of loaded integro-differential equations with involution in the case of degenerate kernels. By applying the parametrization method and the theory of integral equations, the problem is reduced to solving a system of algebraic equations. Based on the invertibility of the matrix of that system, necessary and sufficient conditions for the unique solvability of the problem under study are established.
boundary value problem , Cauchy problem , degenerate kernel , involutory transformation , parametrization method , system of loaded integro-differential equations , unique solvability
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Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, Kazakhstan
Khoja Akhmet Yassawi International Kazakh-Turkish University
10 лет помогаем публиковать статьи Международный издатель
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