Boundary-Value Problem with Pulsed Action. Critical Case of the Second Order

A weakly nonlinear impulsive boundary-value problem is considered in the critical case of the second order. We obtain sufficient conditions of solvability and propose a convergent algorithm for the construction of solutions to these problems. The obtained results agree with the available results of the theory of boundary-value problems for ordinary differential systems and generalize these results to the case of systems with pulsed action.