# Hatvani László honlapja

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 Cím: Stability theorems for nonautonomous functional differential equations by Lyapunov functionals. Szerzõ: Burton, Theodore; Hatvani, L\'aszl\'o Forrás: T\^ohoku Math. J., II. Ser. 41, No.1, 65-104 (1989). Nyelv: English Absztrakt: We consider a system of functional differential equations (1) $x'(t)=F(t,x\sb t)$ having finite delay h and satisfying $F(t,0)=0$. The object is to give conditions on Lyapunov functionals to ensure stability without asking that F(t,$\phi)$ be bounded for $\phi$ bounded. We begin by surveying seven classical examples in which we note that an $L\sp 2$- norm of the solution x(t) frequently appears in the derivative of the Lyapunov functional, but that investigators ignore it in favor of a pointwise norm on x(t). We show that the $L\sp 2$-norm can be much more useful than the pointwise norm. \par A measurable function $\eta$ : $R\to R$ is said to be integrally positive with parameter $\delta >0$ ($\eta\in IP(\delta))$ if whenever $\{t\sb i\}$ and $\{\delta\sb i\}$ satisfy \$t\sb i+\delta\sb i