On the smoothness of solutions of differential equations with a discontinuous right-hand side

A method for the investigation of differential equations with a nonclassical right-hand side [1] is applied to the study of the higher-order differentiability of solutions of differential equations with discontinuous right-hand sides with respect to the initial data. We use results from the theory of differential equations with pulse influence [2].Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1587–1594, December, 1993.