A criterion for unique solvability of a multipoint boundary value problem for systems of integro-differential equations with involution

Abstract

On the interval [0, T], a multipoint boundary value problem is considered for the systems of integrodifferential equations with an involution transformation, when the kernel of the integral term is degenerate. Using the involution property, the problem is reduced to a multipoint boundary value problem for the systems of integro-differential equations with a degenerate kernel. It is shown that by introducing new parameters, changing variables and using the degeneracy of the kernel, the unique solvability of the original problem can be reduced to the inversibility of the resulting matrix.