The Newton—Kantorovich method in the theory of autonomous Noetherian boundary-value problems in the case of parametric resonance - Chuiko, S.M.; Nesmelova, O.V. (Reports of the National Academy of Sciences of Ukraine, 2019)
We have found constructive conditions of solvability and a convergent iterative scheme for constructive solutions of a nonlinear autonomous Noetherian boundary-value problem in the case of parametric resonance. As an example of applying the scheme, some approximations to the solution of a periodic boundary-value problem for an autonomous equation of the Duffing type with a parametric perturbation are determined. To control the accuracy of the approximations, residuals in the original equation are applied.