On a method for construction of successive approximations for investigation of multipoint boundary-value problems

We suggest a new scheme of successive approximations. This scheme allows one to study the problem of existence and approximate construction of solutions of nonlinear ordinary differential equations with multipoint linear boundary conditions. This method enables one to study problems both with singular and nonsingular matrices in boundary conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1243–1253, September, 1995.