Rank criteria for the controllability of a boundary-value problem for a linear system of integro-differential equations with pulse influence

We determine necessary and sufficient conditions for the solvability of boundary-value problems for a linear system of integro-differential equations with pulse influence. We prove theorems on the existence and integral representation of solutions of linear second order integral-sum Volterra equations and linear systems of integro-differential equations with pulse influence at fixed times. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 723–730, June, 2000.