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Perron’s theorem for linear impulsive differential equations with distributed delay. (English) Zbl 1101.34065
The authors show that under a Perron condition, the trivial solution of a linear impulsive differential equation with distributed delay is uniformly asymptotically stable.

MSC:
34K45Functional-differential equations with impulses
34K20Stability theory of functional-differential equations
34K06Linear functional-differential equations
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Full Text: DOI
References:
[1] Angelova, J.; Dishliev, A.; Nenov, S.: I-optimal curve for impulsive Lotka -- Volterra predator -- prey model. Comput. math. Applic. 43, No. 10 -- 11, 1203-1218 (2002) · Zbl 1007.34008
[2] 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
[3] Azbelev, N. V.; Berezanskii, L. M.; Simonov, P. M.; Chistyakov, A. V.: Stability of linear systems with time lag. Differential equations 23, 493-500 (1987) · Zbl 0652.34079
[4] Bellman, R.; Cooke, K. L.: Differential-difference equations. (1963) · Zbl 0105.06402
[5] Berezansky, L.; Braverman, E.: Boundedness and stability of impulsively perturbed systems in a Banach space. Int. J. Theoret. phys. 33, 2075-2091 (1994) · Zbl 0814.34047
[6] Bohl, P.: Riene angew math.. 144, 284-318 (1913)
[7] Gusarenko, S. A.; Domoshnitskii, A. I.: Asymptotic and oscillational properties of first order linear scalar functional differential equations. Differential equations 25, 1480-1491 (1989) · Zbl 0726.45011
[8] Halanay, A.: Differential equationsstability, oscillations, time lags. (1966) · Zbl 0144.08701
[9] Halanay, A.; Wexler, D.: Qualitative theory of impulsive systems. (1968) · Zbl 0176.05202
[10] Hale, J. K.; Lunel, R. M. V.: Introduction to functional differential equations. (1966) · Zbl 0787.34002
[11] Kreyszig, E.: Introductory functional analysis with applications. (1989) · Zbl 0706.46001
[12] Liu, X.; Ballinger, G.: Boundedness for impulsive delay differential equations and applications to population growth models. Nonlinear anal. 53, No. 7 -- 8, 1041-1062 (2003) · Zbl 1037.34061
[13] Nieto, J. J.: Impulsive resonance periodic problems of first order. Appl. math. Lett. 15, No. 4, 489-493 (2002) · Zbl 1022.34025
[14] Perron, O.: Die stabilitatsfrage bei differentialgleichungen. Math. Z. 32, 703-728 (1930) · Zbl 56.1040.01
[15] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations. (1995) · Zbl 0837.34003
[16] Sun, J.; Zhang, Y.; Wu, Q.: Less conservative conditions for asymptotic stability of impulsive control systems. IEEE trans. Automat. control 48, No. 5, 829-831 (2003)
[17] Tang, S.; Chen, L.: Global attractivity in a food-limited population model with impulsive effects. J. math. Anal. appl. 292, No. 1, 211-221 (2004) · Zbl 1062.34055
[18] Tian, Y. P.; Yu, X.; Chua, O. L.: Time-delayed impulsive control of chaotic hybrid systems. Internat. J. Bifur. chaos appl. Sci. eng. 14, No. 3, 1091-1104 (2004) · Zbl 1129.93515
[19] Tyshkevich, V. A.: A perturbations -- accumulation problem for linear differential equation with time lag. Differential equations 14, 177-186 (1978) · Zbl 0409.34073
[20] Zhang, S.; Dong, L.; Chen, L.: The study of predator -- prey system with defensive ability of prey and impulsive perturbations on the predator. Chaos solitons fractals 23, No. 2, 631-643 (2005) · Zbl 1081.34041