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On stability of linear delay differential equations under Perron’s condition. (English) Zbl 1217.34117
Summary: The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.

34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations
Full Text: DOI
[1] O. Perron, “Die stabilitätsfrage bei differentialgleichungen,” Mathematische Zeitschrift, vol. 32, no. 1, pp. 703-728, 1930. · JFM 56.1040.01
[2] R. Bellman, “On an application of a Banach-Steinhaus theorem to the study of the boundedness of solutions of non-linear differential and difference equations,” Annals of Mathematics, vol. 49, pp. 515-522, 1948. · Zbl 0031.39902
[3] J. Kloch, “An illustrative example for the Perron condition,” Annales Polonici Mathematici, vol. 35, no. 1, pp. 11-14, 1978. · Zbl 0366.34006
[4] R. Reissig, “A Perron-like stability criterion for linear systems,” Archiv der Mathematik, vol. 34, no. 1, pp. 53-59, 1980. · Zbl 0414.34055
[5] A. Halanay, Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, NY, USA, 1966. · Zbl 0144.08701
[6] M. U. Akhmet, J. Alzabut, and A. Zafer, “Perron’s theorem for linear impulsive differential equations with distributed delay,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 204-218, 2006. · Zbl 1101.34065
[7] A. Anokhin, L. Berezansky, and E. Braverman, “Exponential stability of linear delay impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 193, no. 3, pp. 923-941, 1995. · Zbl 0837.34076
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