| Title:
|
Behaviour of solutions of linear differential equations with delay (English) |
| Author:
|
Diblík, Josef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
31-47 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form \[ \dot{x}(t)= -c(t)x(t-\tau (t)) \qquad \mathrm {{(^*)}}\] with positive function $c(t).$ Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation \[ \dot{y}(t)=\beta (t)[y(t)-y(t-\tau (t))] \] where the function $\beta (t)$ is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of solutions of the second order ordinary differential equation \[ x^{\prime \prime }(t)+a(t)x(t)=0 \] for positive function $a(t)$ in critical case is considered. (English) |
| Keyword:
|
Positive solution |
| Keyword:
|
oscillating solution |
| Keyword:
|
convergent solution |
| Keyword:
|
linear differential equation with delay |
| Keyword:
|
topological principle of Ważewski (Rybakowski’s approach) |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 0914.34065 |
| idMR:
|
MR1629652 |
| . |
| Date available:
|
2009-02-17T10:10:09Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107631 |
| . |
| Reference:
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