The existence of bounded solutions for differential equations in Hilbert spaces. (English) Zbl 0805.47041

Przeradzki, B.

Ann. Pol. Math. 56, No. 2, 103-121 (1992).

The author discusses bounded solutions for the differential equation \[ x'= A(t)x+ r(x,t) \] in some Hilbert space \(H\), where \(A\) is exponentially dichotomic and \(r\) is condensing with respect to some measure of non-compactness.

Reviewer: J.Appell (Würzburg)

MSC:

47E05	General theory of ordinary differential operators
47J05	Equations involving nonlinear operators (general)
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
34G20	Nonlinear differential equations in abstract spaces

Keywords:

bounded solutions; exponentially dichotomic; condensing; measure of non- compactness