Asymptotic behavior of solutions to mixed type differential equations
This work concerns the asymptotic behavior of solutions to the differential equation $$ \dot{x}(t)+\sum_{i=1}^{m}a_i(t)x(r_i(t))+\sum_{j=1}^{n}b_j(t)x(\tau_j(t))=0, $$ where $a_j(t)$ and $b_j(t)$ are real-valued continuous functions and $r_j(t)$ and $\tau_j(t)$ are non-negative functions su...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/210/abstr.html |
| Summary: | This work concerns the asymptotic behavior of solutions to the
differential equation
$$
\dot{x}(t)+\sum_{i=1}^{m}a_i(t)x(r_i(t))+\sum_{j=1}^{n}b_j(t)x(\tau_j(t))=0,
$$
where $a_j(t)$ and $b_j(t)$ are real-valued
continuous functions and $r_j(t)$ and $\tau_j(t)$
are non-negative functions such that
$$\displaylines{
r_i(t)\leq t,\; t\geq t_0,\quad\lim_{t\to \infty}r_i(t)=\infty,\; i=1,\dots,m;\cr
\tau_j(t)\geq t,\; t\geq t_0,\quad\lim_{t\to \infty}\tau_j(t)=\infty,\; j=1,
\dots,n.
}$$ |
|---|---|
| ISSN: | 1072-6691 |