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

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.