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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.

##### MSC:
 34K45 Functional-differential equations with impulses 34D20 Stability of ODE 34A37 Differential equations with impulses
Full Text:
##### References:
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