Hatvani László honlapja

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Cím:On the asymptotic stability of the solutions of functional differential equations.
Szerző:Hatvani, L.
Forrás:Qualitative theory of differential equations, 3rd Colloq., Szeged/Hung. 1988, Colloq. Math. Soc. J\'anos Bolyai 53, 227-238 (1990).
Nyelv:English
Absztrakt:[For the entire collection see Zbl 0695.00015.] \par Nonautonomous functional differential equation is considered in the general case when the right-hand side can be unbounded as a function of time t. Sufficient conditions for the asymptotic stability and uniform asymptotic stability are given via Lyapunov functionals provided that the derivative of the Lyapunov functional is estimated either by $V'(t,x\sb t)\le -\eta (t)W(\vert x(t)\vert)$ or by $V'(t,x\sb t)\le -\eta (t)W(\vert\vert\vert x\sb t\vert\vert\vert)$ where $\eta$ : $R\sb+\to R\sb+$ is measurable, W: $R\sb+\to R\sb+$ is continuous, strictly increasing with $W(0)=0$, and $\vert\vert\vert \cdot \vert\vert\vert$ denotes the $L\sb 2$-norm.} \RV{L.Hatvani 
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