| Contents |
| In this paper, oscillatory and asymptotic behavior of solutions of a class of
nonlinear second order neutral differential equations in several delays with positive
and negative coefficients of the form
\begin{eqnarray*}
\bigg(r_{1}(t)\bigg(x(t)+\sum_{i=1}^{k}p_{i}(t)x(\tau_{i}(t))\bigg)^{\prime}\bigg)^{\prime}
+r_{2}(t)\bigg(x(t)+\sum_{i=1}^{l}q_{i}(t)x(\sigma_{i}(t))\bigg)^{\prime}\nonumber\\
+\sum_{i=1}^{m}s_{i}(t)G\bigg(x(\alpha_{i}(t))\bigg)-\sum_{i=1}^{n}h_{i}(t)H\bigg(x(\beta_{i}(t))\bigg)=0,
\end{eqnarray*}
and
\begin{eqnarray*}
\bigg(r_{1}(t)\bigg(x(t)+\sum_{i=1}^{k}p_{i}(t)x(\tau_{i}(t))\bigg)^{\prime}\bigg)^{\prime}
+r_{2}(t)\bigg(x(t)+\sum_{i=1}^{l}q_{i}(t)x(\sigma_{i}(t))\bigg)^{\prime}\nonumber\\
+\sum_{i=1}^{m}s_{i}(t)G\bigg(x(\alpha_{i}(t))\bigg)-\sum_{i=1}^{n}h_{i}(t)H\bigg(x(\beta_{i}(t))\bigg)=f(t)
\end{eqnarray*}
are studied for $p_{i}(t) \in C^{2}([t_{0}, \infty), \mathbb{R}); i=1,..,k, q_{i}(t) \in C^{1}([t_{0}, \infty), \mathbb{R}); i=1,...,l$. Moreover, using Banach fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of the forced equation. |
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