Further results on the asymptotic behavior of solutions for neutral differential equations
Nour H. M. Alsharif, Başak Karpuz
Received October 28, 2024. Published online October 29, 2025.
Abstract: 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{\dd}{\dd{}t}[x(t)-px(t-\tau)]+q(t)x(t-\sigma)=0\quad\text{for} t\geq{}t_0, \tag{$\star$} where $\tau,\sigma\in\R^+$, $p\in[0,1)$ and $q\in\cnt{}([t_0,\infty),\R_0^+)$. These results differ from most of the existing results in that our results extend to include values of $p\in[\frac12,1)$ for $(\star)$. Besides, the practical applicability of the given results is shown by a numerical example.
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Affiliations: Nour H. M. Alsharif, Department of Mathematics, Graduate School of Natural and Applied Sciences, Dokuz Eylül University, 35210 İzmir, Turkey, e-mail: nhmalsharif@gmail.com; Başak Karpuz (corresponding author), Department of Mathematics, Faculty of Science, Dokuz Eylül University, 35390 İzmir, Turkey, e-mail: bkarpuz@gmail.com
