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Zbl 1198.34176
Raffoul, Youssef N.
Exponential analysis of solutions of functional differential equations with unbounded terms. (English)
[J] Banach J. Math. Anal. 3, No. 2, 28-41, electronic only (2009). ISSN 1735-8787/e

Consider the functional differential equation $x'(t) = G(t, x(s); 0\leq s\leq t)$, where $x\in {\Bbb R}^n$ and $G$ is a continuous functional. In this paper, the boundedness of solutions of the above equation is studied and sufficient conditions are obtained by using the methods of Lyapunov functionals. Volterra integro-differential equations are given to illustrate the theorems.
[Zhanyuan Hou (London)]

MSC 2000:: *34K30 Functional-differential equations in abstract spaces
34K20 Stability theory of functional-differential equations
34K12 Properties of solutions of functional-differential equations

Keywords: nonlinear differential systems; boundedness; uniform boundedness; Lyapunov functionals; Volterra integro-differential equations

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