Geodesic
Asymptotic estimation of the convergence of solutions of the equation $\dot x(t)=b(t) x(t-\tau (t))$
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 279-287

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The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x}(t)=b(t)x(t-\tau (t))$. Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x(t)$ reaches an $\varepsilon $ - neighbourhood of origin and remains in it.
The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x}(t)=b(t)x(t-\tau (t))$. Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x(t)$ reaches an $\varepsilon $ - neighbourhood of origin and remains in it.
Classification : 34K20, 34K25
Keywords: stability of trivial solution; estimation of convergence of nontrivial solutions 
Diblík, Josef; Khusainov, Denys. Asymptotic estimation of the convergence of solutions of the equation $\dot x(t)=b(t) x(t-\tau (t))$. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 279-287. http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a3/
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     title = {Asymptotic estimation of the convergence of solutions of the equation $\dot x(t)=b(t) x(t-\tau (t))$},
     journal = {Archivum mathematicum},
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     year = {2001},
     volume = {37},
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     mrnumber = {1879450},
     zbl = {1090.34059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a3/}
}
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