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Zbl 1047.34094
Akhmet, M. U.
On the general problem of stability for impulsive differential equations.
(English)
[J] J. Math. Anal. Appl. 288, No. 1, 182-196 (2003). ISSN 0022-247X

This paper is devoted to criteria for stability, asymptotical stability and instability of nontrivial solutions of the impulsive system $$\gathered {dx\over dt}= f(t,x),\quad t\ne \theta_i(x),\\ \Delta x\vert_{t=\theta_i(x)}= I_i(x),\quad i\in\bbfN= \{1,2,\dots\},\endgathered\tag1$$ with $\Delta x\vert_{t=\theta}= x(\theta+)- x(\theta)$, $x(\theta+)= \lim_{t\to\theta^+}\, x(t)$, obtained by Lyapunov's second method. The author indicates that a construction of a reduced system for (1) with variable time of impulsive action is done for the first time.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*34K45 Equations with impulses
34D20 Lyapunov stability of ODE
34A37 Differential equations with impulses

Keywords: Stability; Instability; Reduced system; Lyapunov's second method; Impulse system; Asymptotical stability; Impulsive action

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