The conditions for the existence of solutions of nonlinear differential equations in a space of functions bounded on the axis are established by using local linear approximations of these equations.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1541–1556, November, 2009.
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Slyusarchuk, V.Y. Method of local linear approximation in the theory of bounded solutions of nonlinear differential equations. Ukr Math J 61, 1809–1829 (2009). https://doi.org/10.1007/s11253-010-0314-x
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DOI: https://doi.org/10.1007/s11253-010-0314-x