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Cím:On the asymptotic stability for functional differential equations by Lyapunov functionals.
Szerző:Hatvani, L.
Forrás:Nonlinear Anal., Theory Methods Appl. 40A, No.1-8, 251-263 (2000)
Nyelv:English
Absztrakt:The author considers the nonautonomous system $$x'(t)=F(t,x_t),\ F(t,0)\equiv 0,\tag 1$$ where $C=C([-h,0];\bbfR^n)$ denotes the space of continuous functions from $[-h,0]$ into $\bbfR^n,\ 0<h=\text{const.}$; $F:\bbfR_{+}\times C\to\bbfR^n$ is continuous and maps bounded sets into bounded sets. For any solution $x:[t_0-h,T]\to\bbfR^n$ and any $t\in [t_0,T]$, the segment $x_t\in C$ is defined by $x_t(s):=x(t+s),\ -h\leq s\leq 0$.\par The paper is concerned with conditions of different kinds of stability of the zero solution to (1). The main tool in the stability investigations is Lyapunov's direct method.} \RV{J.Ohriska (Ko\v{s}ice) 
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