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Keywords:
neutral differential equation; uniform stability; globally attractivity; globally asymptotic stability
neutral differential equation; uniform stability; globally attractivity; globally asymptotic stability
Summary:
This paper focuses on the uniform stability of the zero solution and the asymptotic behavior of all solutions in the context of the neutral differential equation $$ \frac {\mathrm{d} }{\mathrm{d} t}[x(t)-px(t-\tau )]+q(t)x(t-\sigma )=0\quad \text {for}\ t\geq t_{0}, $$ where $\tau ,\sigma \in \mathbb{R} ^{+}$, $p\in [0,1)$ and $q\in {{\rm C}^{\#1}} ([t_{0},\infty ),\mathbb{R} _{0}^{+})$. These results differ from most of the existing results in that our results extend to include values of $p\in [\frac {1}{2},1)$ for $(\star )$. Besides, the practical applicability of the given results is shown by a numerical example.
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