Chuiko A. Impulse boundary problem for the system of differential equations with switchings

The scheme for investigation the problems concerning the existence and construction solutions of Noetherian boundary problems for nonlinear system for the ordinary differential equation has been improved. The constructive estimates for the lenth of the segment have been received. On this segment small parameter changes and the convergence of the iteration procedure for the sought solution of semi-nonlinear problem remains for the system of the ordinary differential equations both in the critical and noncritical cases. Necessary and sufficient conditions for the existence and construction of the iteration procedure for finding the solution of semi-nonlinear problems in the unusually critical case have been found. Green's operator for Cauchy's problem for linear system of the differential equation with switchings and impulse perturbation of "interface conditions" type has been constructed. Green's operator for the general Noetherian problem for linear system of differential equations with switchings and impulse perturbation of "interface conditions" type has been obtained. The constructive conditions for existence of solutions Noetherian semi-nonlinear boundary-value problem for the linear system of the differential equations with switchings and impulse perturbation of "interface conditions" type have been proved. Convergent iteration algorithms for the construction of the solutions of Noetherian semi-nonlinears boundary-value have been proposed.