CRITERIA FOR DICHOTOMY OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS

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Published: Jun 1, 1994
DOI: https://doi.org/10.5556/j.tkjm.25.1994.4431
Keywords:
Dichotomy impulsive differential equations

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P. S. SIMEONOV
Plovdiv University, Paissii Hilendarski.
D. D. BAINOV
South-West University, Blagoevgrad, Bulgaria.

Abstract




In the present paper necessary and sufficient conditions for $(\mu_1, \mu_2)$- dichotomy of linear impulsive differential equations are obtained without imposing conditions of bounded growth on these equations. The apparatus of piecewise continuous Lyapunov's functions is used.




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How to Cite
SIMEONOV, P. S., & BAINOV, D. D. (1994). CRITERIA FOR DICHOTOMY OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS. Tamkang Journal of Mathematics, 25(2), 101–112. https://doi.org/10.5556/j.tkjm.25.1994.4431
Issue
Vol. 25 No. 2 (1994)
Section
Papers
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References

D. D. Bainov and P. S. Simeonov, Stability Theory of Differential Equations with Impulse Effect: Theory and Applications, Ellis Horwood, 1989.

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J. S. Muldowney, "Dichotomies and asymptotic behaviour for linear differential systems," Transactions of the Amer. Math. Soc., vol 283, No 2 (1984), 465-484.

P. S. Simeonov and D. D. Bainov., "Stability with respect to part of the variables in systems with impulse effect," J. Math. Anal. Appl. 117, No. 1 (1986), 247-263.

T. Yoshizawa, Stability theory by Liapunov's second method, Math. Soc. Japan, Tokyo, 1966.