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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 134072, 9 pages
On Stability of Linear Delay Differential Equations under Perron's Condition
1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno 602 00, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno 616 00, Czech Republic
3Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Received 18 January 2011; Accepted 22 February 2011
Academic Editor: Miroslava Růžičková
Copyright © 2011 J. Diblík and A. Zafer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- O. Perron, “Die stabilitätsfrage bei differentialgleichungen,” Mathematische Zeitschrift, vol. 32, no. 1, pp. 703–728, 1930.
- 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.
- J. Kloch, “An illustrative example for the Perron condition,” Annales Polonici Mathematici, vol. 35, no. 1, pp. 11–14, 1978.
- R. Reissig, “A Perron-like stability criterion for linear systems,” Archiv der Mathematik, vol. 34, no. 1, pp. 53–59, 1980.
- A. Halanay, Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, NY, USA, 1966.
- 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.
- 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.