3 research outputs found
Necessary and sufficient conditions for the oscillation of higher-order differential equations involving distributed delays
In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation
\begin{equation}
\bigg[x(t)+\int_{0}^{\lambda}p(t,v)x(\tau(t,v))\,\mathrm{d}v\bigg]^{(n)}+\int_{0}^{\lambda}q(t,v)x(\sigma(t,v))\,\mathrm{d}v=\varphi(t)\quad\text{for } t \geq t_{0},\notag
\end{equation}
where , , , , with and for all , with , and . We also give illustrating examples to show the applicability of these results
Oscillation of first-order neutral differential equations with distributed deviating arguments
WOS: 000253509100015In this paper we shall consider first-order neutral differential equations with distributed deviating arguments. Some new sufficient conditions are presented for the oscillation of all solutions. (c) 2007 Elsevier Ltd. All rights reserved