On solutions defined on an axis for differential equations with shifts of the argument - Chaikovs'kyi, A. V.; Чайковський, А. В. (Institute of Mathematics, NAS of Ukraine, 2011)
We consider linear first-order differential equations with shifts of arguments with respect to 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 an axis are solutions of a given equation with shifts of the argument.