Domain of Convergence of an Iteration Procedure for a Weakly Nonlinear Boundary-Value Problem

We obtain estimates for the values of a small parameter for which the iteration procedure used for the construction of solutions of the Noetherian weakly nonlinear boundary-value problem for a system of ordinary differential equations is convergent in both critical and noncritical cases. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 278–288, April–June, 2005.