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On the general problem of stability for impulsive differential equations. (English) Zbl 1047.34094
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.

34K45Functional-differential equations with impulses
34D20Stability of ODE
34A37Differential equations with impulses
Full Text: DOI
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