On the Unique Solvability of a Boundary Value Problem for Systems of Loaded Integro-Differential Equations with Involution.

Autor: Usmanov, K. I., Nazarova, K. Zh., Yerkisheva, Zh. S.
Zdroj: Lobachevskii Journal of Mathematics; Dec2021, Vol. 42 Issue 12, p3022-3034, 13p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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