We consider linear first-order differential equations with shifts of the argument for functions with values in a Banach space. Sufficient conditions for the existence of nontrivial solutions of homogeneous equations are obtained. Ordinary differential equations are constructed for which all solutions defined on the entire axis are solutions of a given equation with shifts of the argument.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1290–1296, September, 2011.
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Chaikovs’kyi, A.V. On solutions defined on an axis for differential equations with shifts of the argument. Ukr Math J 63, 1470–1477 (2012). https://doi.org/10.1007/s11253-012-0593-5
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DOI: https://doi.org/10.1007/s11253-012-0593-5