Criteria for the unique solvability of a linear two-point boundary value problem for systems of integro-differential equations

Abstract

For a linear boundary value problem for a Fredholm integro-differential equation, we obtain necessary and sufficient conditions for the unique solvability in terms of a matrix Qνm (h) formed on the basis of the matrices of boundary conditions, the differential part, the integral term, and a partition with increment h > 0 of the interval on which the problem is defined.