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Keywords:
third-order; neutral functional differential equations; oscillation and asymptotic behavior
third-order; neutral functional differential equations; oscillation and asymptotic behavior
Summary:
The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation
\begin{equation*} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^{\prime \prime }\big )^\alpha \big ]^{\prime }+q(t)x^\alpha (\tau (t))=0\,, E \end{equation*}
where $\alpha >0$, $0\le p(t)\le p_0<\infty $ and $\delta (t)\le t$. By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.
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