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Necessary and sufficient conditions for the existence of solutions of weakly nonlinear boundary-value problem of systems of integrodifferential equations with impulsive action at fixed points of time are obtained. Convergent iterative procedure of the solution and establish the connection between the necessary condition and the sufficient condition are presented. 2010 Mathematics Subject Classification: 34B15; 34B37

Weakly nonlinear impulsive boundary value problems for systems of integrodifferential equations