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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.

MSC:

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