Uniformly bounded solutions of functional differential equations. (English) Zbl 0807.34084
The author proves the uniform boundedness and the ultimate uniform boundedness of the solutions of the system of functional differential equations \(x'= f(t,x_ t)\), where \(x_ t(s)= x(t+ s)\), \(-h\leq s\leq 0\), \(f: \mathbb{R}_ +\times C\to \mathbb{R}^ n\), \(C\) is the space of continuous functions \(\varphi: [-h,0]\to \mathbb{R}^ n\).
Reviewer: A.H.Nasr
MSC:
34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
34D40 | Ultimate boundedness (MSC2000) |