Asymptotic properties of solutions to linear nonhomogeneous differential equations with variable delays and variable coefficients

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Abstract

In this paper, we examine the asymptotic properties of solutions to first-order linear non- homogeneous differential equations with variable delays and variable coefficients. Initially, a unique global solution to the relevant characteristic equation is obtained. Subsequently, the asymptotic prop- erties of the solutions to the delay equation are demonstrated through the utilization of the solution of the characteristic equation. Finally, upon examination of specific cases pertaining to the variable coef- ficients of the delay differential equation, three discrete results are obtained. The findings are expressed as the solution of the characteristic equation. In addition, seven examples are given to demonstrate the hypothesis of the main theorem.

Keywords

delay differential equation / nonhomogeneous equation / asymptotic behavior / characteristic equation

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