| Title:
|
Solutions of an advance-delay differential equation and their asymptotic behaviour (English) |
| Author:
|
Vážanová, Gabriela |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
141-149 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper considers a scalar differential equation of an advance-delay type \begin{equation*} \dot{y}(t)= -\left(a_0+\frac{a_1}{t}\right)y(t-\tau )+\left(b_0+\frac{b_1}{t}\right)y(t+\sigma )\,, \end{equation*} where constants $a_0$, $b_0$, $\tau $ and $\sigma $ are positive, and $a_1$ and $b_1$ are arbitrary. The behavior of its solutions for $t\rightarrow \infty $ is analyzed provided that the transcendental equation \begin{equation*} \lambda = -a_0\mathrm{e}^{-\lambda \tau }+b_0\mathrm{e}^{\lambda \sigma } \end{equation*} has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution. (English) |
| Keyword:
|
advance-delay differential equation |
| Keyword:
|
mixed-type differential equation |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
existence of solutions |
| MSC:
|
34K12 |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 07675583 |
| idMR:
|
MR4563025 |
| DOI:
|
10.5817/AM2023-1-141 |
| . |
| Date available:
|
2023-02-22T14:37:32Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151559 |
| . |
| 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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| . |
