On Approximate Solutions of Nonlinear Boundary-Value Problems by the Newton–Kantorovich Method

We establish necessary and sufficient conditions for the solvability of nonlinear boundary-value problem in critical case develop a scheme construction solutions this problem. By using Newton–Kantorovich method, we propose new iterative determination to weakly system ordinary differential equations case. As examples application constructed scheme, obtain approximations periodic Duffing Lienard equations. To check accuracy established equations, use discrepancies original