Liubyma O. Newton-Kantorovich's method of autonomous boundary value problems

The thesis is devoted to the problem of finding constructive conditions of existence and construction of solutions of autonomous nonlinear Noetherian boundary-value problems for the systems of differential equations. On the basis of the theory of pseudoinverse matrixes, theory methods of perturbation and of the Newton-Kantorovich's method at thesis improved scheme for studying problems of the existence and the construction of solutions of Noetherian autonomous boundary-value problems for nonlinear systems of ordinary differential equations in the critical cases. We find the necessary and sufficient conditions for the existence and constructed modified iterative procedure using least-squares method for finding solutions of Noetherian semi-nonlinear boundary-value problems.