Solutions of an advance-delay differential equation and their asymptotic behaviour

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F23%3APU149294" target="_blank" >RIV/00216305:26220/23:PU149294 - isvavai.cz</a>
Result on the web
<a href="https://dml.cz/handle/10338.dmlcz/151559" target="_blank" >https://dml.cz/handle/10338.dmlcz/151559</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5817/AM2023-1-141" target="_blank" >10.5817/AM2023-1-141</a>

Result language
angličtina
Original language name
Solutions of an advance-delay differential equation and their asymptotic behaviour
Original language description
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 $trightarrow infty $ is analyzed provided that the transcendental equation begin{equation*} lambda = -a_0mathrm{e}^{-lambda tau }+b_0mathrm{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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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