Geodesic
Solutions of an advance-delay differential equation and their asymptotic behaviour
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 141-149

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.5817/AM2023-1-141
Classification : 34K12, 34K25
Keywords: advance-delay differential equation; mixed-type differential equation; asymptotic behaviour; existence of solutions 
@article{10_5817_AM2023_1_141,
     author = {V\'a\v{z}anov\'a, Gabriela},
     title = {Solutions of an advance-delay differential equation and their asymptotic behaviour},
     journal = {Archivum mathematicum},
     pages = {141--149},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2023},
     doi = {10.5817/AM2023-1-141},
     mrnumber = {4563025},
     zbl = {07675583},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-141/}
}
TY  - JOUR
AU  - Vážanová, Gabriela
TI  - Solutions of an advance-delay differential equation and their asymptotic behaviour
JO  - Archivum mathematicum
PY  - 2023
SP  - 141
EP  - 149
VL  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-141/
DO  - 10.5817/AM2023-1-141
LA  - en
ID  - 10_5817_AM2023_1_141
ER  - 
%0 Journal Article
%A Vážanová, Gabriela
%T Solutions of an advance-delay differential equation and their asymptotic behaviour
%J Archivum mathematicum
%D 2023
%P 141-149
%V 59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-141/
%R 10.5817/AM2023-1-141
%G en
%F 10_5817_AM2023_1_141
Vážanová, Gabriela. Solutions of an advance-delay differential equation and their asymptotic behaviour. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 141-149. doi: 10.5817/AM2023-1-141

Cité par Sources :