A nonlinear two-point boundary-value problem for an ordinary differential equation is studied by the method of parametrization. We construct systems of nonlinear algebraic equations that enable us to find the initial approximation to the solution to the posed problem. In terms of the properties of constructed systems, we establish necessary and sufficient conditions for the existence of an isolated solution to the analyzed boundary-value problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 3, pp. 356–365, March, 2018.
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Dzhumabaev, D.S., Temesheva, S.M. Criteria for the Existence of an Isolated Solution of a Nonlinear Boundary-Value Problem. Ukr Math J 70, 410–421 (2018). https://doi.org/10.1007/s11253-018-1507-y
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DOI: https://doi.org/10.1007/s11253-018-1507-y