ON A CONNECTION BETWEEN A CLASS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL OPERATORS WITH SEMI-SEPARABLE KERNEL

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Submitted: 2025-01-31; Published: 2025-01-31

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Abstract

In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.