On the existence of bounded solutions of nonlinear differential equations in Banach spaces. (English) Zbl 0617.34061

Szufla, Stanisław

Funct. Approximatio, Comment. Math. 15, 117-123 (1986).

Author’s summary: ”In this paper we give sufficient conditions for the existence of bounded solutions of the differential equation \(\dot x=A(t)x+f(t,x)\) in a Banach space. Our assumptions are formulated in terms of Orlicz spaces and measures of noncompactness.”

Reviewer: E.Heil

MSC:

34G10	Linear differential equations in abstract spaces
34C11	Growth and boundedness of solutions to ordinary differential equations

Keywords:

first order differential equation; bounded solutions; Banach space; Orlicz spaces; measures of noncompactness