We establish necessary and sufficient conditions for the existence of solutions of an autonomous Noetherian boundary-value problem for a system of second-order ordinary differential equations in the critical case. For the construction of solutions of a nonlinear Noetherian boundary-value problem in the critical case, we propose an iterative scheme that combines the Newton–Kantorovich method and the leastsquares technique. The efficiency of the proposed method is demonstrated in the analysis of a periodic problem for a Liénard-type equation.
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Translated from Neliniini Kolyvannya, Vol. 15, No. 2, pp. 274–288, April–June, 2012
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Chuiko, S.M., Boichuk, I.A. & Pirus, O.E. On the approximate solution of an autonomous boundary-value problem by the Newton–Kantorovich method. J Math Sci 189, 867–881 (2013). https://doi.org/10.1007/s10958-013-1225-9
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DOI: https://doi.org/10.1007/s10958-013-1225-9