Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]