Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 0801.34076
Malygina, V.V.
Some criteria for stability of equations with retarded argument. (English. Russian original)
[J] Differ. Equations 28, No.10, 1398-1405 (1992); translation from Differ. Uravn. 28, No.10, 1716-1723 (1992). ISSN 0012-2661

The author considers the delay differential equation $(*)$ $\dot x(t)+ \int\sp t\sb \tau [d\sb s R(t,s)] x(s)=0$, $t\ge \tau$ $(\tau\in \bbfR\sb +)$, where $R: \{(t,s)\in \bbfR\sb +\times \bbfR\sb +$: $t\ge s\}\to L(B)$ is such that $R(\cdot,s)$ is Bochner-integrable on any finite interval of $\bbfR\sb +$ and $R(t,\cdot)$ is a function of bounded variation on any compact interval $[0,T]$. Here $L(B)$ denotes the set of the bounded linear operators on a Banach space $B$. In the paper, there are some nice results concerning the stability, exponential stability and asymptotic stability of the zero solution of equation $(*)$. These results are based on some simple but interesting exponential estimates of the fundamental solution of $(*)$. Some special examples are also discussed.

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K30 Functional-differential equations in abstract spaces

Keywords: delay differential equation; exponential stability; asymptotic stability; exponential estimates

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

	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]