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

Zuev, A. L.

Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2007, No. 2, 7-12 (2007).

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

Keywords:

linear differential equation; perturbation; infinitesimal generator