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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.

34K20Stability theory of functional-differential equations
34K06Linear functional-differential equations
Full Text: DOI
[1] O. Perron, “Die stabilitätsfrage bei differentialgleichungen,” Mathematische Zeitschrift, vol. 32, no. 1, pp. 703-728, 1930. · Zbl 56.1040.01 · doi:10.1007/BF01194662
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[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 · doi:10.1016/j.cam.2005.06.004
[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 · doi:10.1006/jmaa.1995.1275