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The solvability of an impulse BVP (IBVP) for a system of integro-differential equations with a degenerate kernel is studied when assuming that the IBVP does not have a solution for arbitrary inhomogeneities. To reduce it to a solvable form, a control function is introduced, a solvability criterion is established, and its general form is constructed. The fact that the control may not be unique admits using it to study problems that are often encountered in the optimal control theory. The adopted method employs the theory of pseudoinverse matrices (in the Moore-Penrose sense) and orthoprojectors.

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Regularization of Linear Impulsive Boundary Value Problem for Systems of Integro-Differential Equations

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  • 发表日期：

    2025年

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  • Ivanna Bondar

摘要

The solvability of an impulse BVP (IBVP) for a system of integro-differential equations with a degenerate kernel is studied when assuming that the IBVP does not have a solution for arbitrary inhomogeneities. To reduce it to a solvable form, a control function is introduced, a solvability criterion is established, and its general form is constructed. The fact that the control may not be unique admits using it to study problems that are often encountered in the optimal control theory. The adopted method employs the theory of pseudoinverse matrices (in the Moore-Penrose sense) and orthoprojectors.