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Piriadarshani, D.; Sengadir, T.

Asymptotic stability of differential equations with infinite delay. (English) Zbl 1247.34123

J. Appl. Math. 2012, Article ID 804509, 10 p. (2012).

MSC:

34K20 Stability theory of functional-differential equations
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\textit{D. Piriadarshani} and \textit{T. Sengadir}, J. Appl. Math. 2012, Article ID 804509, 10 p. (2012; Zbl 1247.34123)
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References:

[1] J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 11-41, 1978. · Zbl 0383.34055
[2] J. Kato, “Stability problem in functional differential equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 63-80, 1978. · Zbl 0413.34076
[3] F. V. Atkinson and J. R. Haddock, “On determining phase spaces for functional-differential equations,” Funkcialaj Ekvacioj, vol. 31, no. 3, pp. 331-347, 1988. · Zbl 0665.45004
[4] Y. Hino, S. Murakami, and T. Naito, Functional-Differential Equations with Infinite Delay, vol. 1473, Springer, Berlin, Germany, 1991. · Zbl 0732.34051
[5] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99, Springer, New York, NY, USA, 1993. · Zbl 0787.34002
[6] J. R. Haddock, M. N. Nkashama, and J. H. Wu, “Asymptotic constancy for linear neutral Volterra integrodifferential equations,” The Tohoku Mathematical Journal, vol. 41, no. 4, pp. 689-710, 1989. · Zbl 0688.45010
[7] M. De la Sen, “Sufficiency-type stability and stabilization criteria for linear time-invariant systems with constant point delays,” Acta Applicandae Mathematicae, vol. 83, no. 3, pp. 235-256, 2004. · Zbl 1067.34078
[8] X. Liu, S. Zhong, and X. Ding, “Robust exponential stability of impulsive switched systems with switching delays: a razumikhin approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1805-1812, 2012. · Zbl 1239.93104
[9] R. Datko, “Remarks concerning the asymptotic stability and stabilization of linear delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 111, no. 2, pp. 571-584, 1985. · Zbl 0579.34052
[10] T. Sengadir, “Discretisation of an infinite delay equation,” Mathematics of Computation, vol. 76, no. 258, pp. 777-793, 2007. · Zbl 1116.34060
[11] D. Piriadarshani and T. Sengadir, “Numerical solution of a neutral differential equation with infinite delay,” Differential Equations and Dynamical Systems, vol. 20, no. 1, pp. 17-34, 2012. · Zbl 1270.34177
[12] O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel, and H.-O. Walther, Delay Equations, vol. 110, Springer, New York, NY, USA, 1995. · Zbl 0826.34002
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