About one boundary value problem for linear integro-differential equations

Abstract

In [1], [2], [3] we have investigated solutions of some classes of linear integro-differential equations. At the same time, both general solutions and solutions of the Cauchy problem were found for the mentioned types of equations. The method we used in the cited papers can be successfully applied to the solution of the boundary value problem for linear integro-differential equations. Part of the eigennumbers of the integro-differential system (2) at m≤n. are the eigennumbers of the integral equation (32), and another part of them are the roots of the equation D (X) = 0. Together they form the spectrum of eigennumbers of the integro-differential system (2). It follows that the spectrum of eigennumbers of an integro-differential system is a discrete set.