Asymptotic Properties of Solutions to Linear Non-Homogeneous Neutral-Delay Differential Equations with Variable Delays and Coefficients

This article investigates the asymptotic properties of the solutions to first-order linear non-homogeneous neutral-delay differential equations that have variable coefficients and variable delays. Firstly, the aforementioned asymptotic properties were established using the solution of the characteristic equation. Subsequently, by examining specific cases regarding the variable coefficients of the neutral-delay differential equation, two distinct results were obtained. Finally, as a special case, the linear non-homogeneous neutral-delay differential equation with constant coefficients and delays was considered. The findings are presented in terms of the solution to the characteristic equation. Furthermore, nine examples are provided to elaborate on the finding that the hypotheses examined in the main theorem and in the special case hold.