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Title: Asymptotic estimation of the convergence of solutions of the equation $\dot x(t)=b(t) x(t-\tau (t))$ (English)
Author: Diblík, Josef
Author: Khusainov, Denys
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 37
Issue: 4
Year: 2001
Pages: 279-287
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: stability of trivial solution
Keyword: estimation of convergence of nontrivial solutions
MSC: 34K20
MSC: 34K25
idZBL: Zbl 1090.34059
idMR: MR1879450
Date available: 2008-06-06T22:29:08Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Bellman R., Cooke K. L.: Differential-Difference Equations.Acad. Press, New-York-London, 1963. Zbl 0105.06402, MR 0147745
Reference: [2] Čermák J.: The asymptotic bounds of solutions of linear delay systems.J. Math. Anal. Appl. 225 (1998), 373–338. MR 1644331
Reference: [3] Diblík J.: Stability of the trivial solution of retarded functional equations.Differ. Uravn. 26 (1990), 215–223. (In Russian).
Reference: [4] Elsgolc L. E., Norkin S. B.: Introduction to the Theory of Differential Equations with Deviating Argument.Nauka, Moscow, 1971. (In Russian). MR 0352646
Reference: [5] Györi I., Pituk M.: Stability criteria for linear delay differential equations.Differential Integral Equations 10 (1997), 841–852. Zbl 0894.34064, MR 1741755
Reference: [6] Hale J., Lunel S. M. V.: Introduction to Functional Differential Equations.Springer-Verlag, 1993. Zbl 0787.34002, MR 1243878
Reference: [7] Kolmanovskij V., Myshkis A.: Applied Theory of Functional Differential Equations.Kluwer Acad. Publ., 1992. Zbl 0785.34005, MR 1256486
Reference: [8] Kolmanovskij V., Myshkis A.: Introduction to the Theory and Applications of Functional Differential Equations.Kluwer Acad. Publ., 1999. Zbl 0917.34001, MR 1680144
Reference: [9] Kolmanovskij V. B., Nosov V. R.: Stability and Periodic Modes of Regulated Systems with Delay.Nauka, Moscow, 1981. (In Russian).
Reference: [10] Krasovskii N. N.: Stability of Motion.Stanford Univ. Press, 1963. Zbl 0109.06001, MR 0147744
Reference: [11] Krisztin T.: Asymptotic estimation for functional differential equations via Lyapunov functions.Colloq. Math. Soc. János Bolyai, Qualitative Theory of Differential Equations, Szeged, Hungary, 1988, 365–376. MR 1062660
Reference: [12] Myshkis A. D.: Linear Differential Equations with Delayed Argument.Nauka, Moscow, 1972. (In Russian). MR 0352648
Reference: [13] Pituk M.: Asymptotic behavior of solutions of differential equation with asymptotically constant delay.Nonlinear Anal. 30 (1997), 1111–1118. MR 1487679
Reference: [14] Razumikhin B. S.: Stability of Hereditary Systems.Nauka, Moscow, 1988. (In Russian). MR 0984127


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