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Oscillation and stability of linear impulsive delay differential equations. (English) Zbl 0917.34060
Summary: The main results are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses. The results can be used to improve and derive some known results. $\copyright$ Academic Press.

34K20Stability theory of functional-differential equations
34A37Differential equations with impulses
34K11Oscillation theory of functional-differential equations
Full Text: DOI
[1] Anokhin, A.; Berezansky, L.; Braverman, E.: Exponential stability of linear delay impulsive differential equations. J. math. Anal. appl. 193, 923-941 (1995) · Zbl 0837.34076
[2] Berezansky, L.; Braverman, E.: Oscillation of a linear delay impulsive differential equation. Comm. appl. Nonlinear anal. 3, 61-77 (1996) · Zbl 0858.34056
[3] Chen, M. P.; Yu, J. S.; Shen, J. H.: The persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations. Comput. math. Appl. 27, 1-6 (1994) · Zbl 0806.34060
[4] Domoshnitsky, A.; Drakhlin, M.: Nonoscillation of first order impulsive differential equations with delay. J. math. Anal. appl. 106, 254-269 (1997) · Zbl 0870.34010
[5] Gopalsamy, K.; Zhang, B. G.: On delay differential equation with impulses. J. math. Anal. appl. 139, 110-122 (1989) · Zbl 0687.34065
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[8] Shen, J. H.: The nonoscillatory solutions of delay differential equations with impulses. Appl. math. Comput. 77, 153-165 (1996) · Zbl 0861.34044
[9] Yu, J. S.: Stability caused by impulses for delay differential equations. Acta math. Sinica (N.S.) 13, 193-198 (1997) · Zbl 0881.34080
[10] Yu, J. S.; Zhang, B. G.: Stability theorem for delay differential equations with impulses. J. math. Anal. appl. 199, 162-175 (1996) · Zbl 0853.34068
[11] Zhao, A.; Yan, J.: Existence of positive solutions for delay differential equations with impulses. J. math. Anal. appl. 210, 667-678 (1997) · Zbl 0878.34060
[12] Zhao, A.; Yan, J.: Asymptotic behavior of solutions of impulsive delay differential equations. J. math. Anal. appl. 201, 943-954 (1996) · Zbl 0873.34063