Asymptotic behaviour of solutions of some differential equations with an unbounded delay
We investigate the asymptotic properties of all solutions of the functional differential equation $$\dot{x}(t)=p(t)[x(t)-kx(t-\tau (t))]+q(t),\qquad t\in I=[t_0,\infty),$$ where $k\ne 0$ is a scalar and $\tau (t)$ is an unbounded delay. Under certain restrictions we relate asymptotic behaviour of s...
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| Format: | Article |
| Language: | English |
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University of Szeged
2000-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=31 |
| Summary: | We investigate the asymptotic properties of all solutions of the functional differential equation
$$\dot{x}(t)=p(t)[x(t)-kx(t-\tau (t))]+q(t),\qquad t\in I=[t_0,\infty),$$
where $k\ne 0$ is a scalar and $\tau (t)$ is an unbounded delay. Under certain restrictions we relate asymptotic behaviour of solutions $x(t)$ of this equation to the behaviour of a solution $\varphi (t)$ of the auxiliary functional nondifferential equation
$$\varphi (t)=|k|\,\varphi (t-\tau (t)),\qquad t\in I.$$ |
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| ISSN: | 1417-3875 |