Об относительной компактности траекторий дифференциальных уравнений в банаховом пространстве

Abstract

A class of bounded perturbations of a linear differential equation in a Banach space is considered. Sufficient conditions for the precompactness of trajectories of the perturbed system are proposed. Such conditions are shown to be applicable for a nonlinear differential equation without assuming that the corresponding infinitesimal generator is accretive.