| Title:
|
Asymptotic behaviour of solutions of some linear delay differential equations (English) |
| Author:
|
Čermák, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
355-364 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the asymptotic properties of all solutions of the delay differential equation
y'(x)=a(x)y(\tau(x))+b(x)y(x),\qquad x\in I=[x_0,\infty).
We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation
z'(x)=b(x)z(x),\qquad x\in I
and a solution of the functional equation
|a(x)|\varphi(\tau(x))=|b(x)|\varphi(x),\qquad x\in I. (English) |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
differential equation |
| Keyword:
|
delayed argument |
| Keyword:
|
functional equation |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
39B05 |
| MSC:
|
39B22 |
| MSC:
|
39B99 |
| idZBL:
|
Zbl 0972.34066 |
| idMR:
|
MR1790126 |
| DOI:
|
10.21136/MB.2000.126125 |
| . |
| Date available:
|
2009-09-24T21:44:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126125 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[9] T. Kato J. B. McLeod: The functional differential equation $y'(x) = a y(\lambda x) + b y(x).Bull. Amer. Math. Soc. 77 (1971), 891-937. MR 0283338 |
| Reference:
|
[10] M. Kuczma B. Choczewski R. Ger: Iterative Functional Equations.Encyclopedia of Mathematics and Its Applications, Cambridge Univ. Press, Cambridge, England, 1990. MR 1067720 |
| Reference:
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| Reference:
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| . |
