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Unified boundedness, periodicity, and stability in ordinary and functional differential equations. (English) Zbl 0626.34038

The uniform boundedness and uniform ultimate boundedness in connection with stability, uniform asymptotic stability, equi-asymptotic stability and periodicity of solutions to a system of ordinary differential equations \(x'=F(t,x)\), with continuous right-hand side are studied. The common differential equations, equations with both bounded and unbounded delay as well as the systems with unbounded initial function are considered. Many examples illustrate the main theorems.
Reviewer: D.Babrowski

MSC:

34C25 Periodic solutions to ordinary differential equations
34D40 Ultimate boundedness (MSC2000)
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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