On the relative compactness of the trajectories of differential equations in a Banach space. (Russian. English summary) Zbl 1121.34326

Summary: 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 to a nonlinear differential equation without assuming that the corresponding infinitesimal generator is accretive.


34G10 Linear differential equations in abstract spaces
47E05 General theory of ordinary differential operators
34D10 Perturbations of ordinary differential equations