Periodic solutions and asymptotic properties of first order linear nonhomogeneous neutral delay differential equations

This article concerns first-order linear nonhomogeneous neutral delay differential equations with periodic coefficients and constant delays, where the coefficients share a common period and the delays are multiples of this period. First, we obtain periodic solutions of linear nonhomogeneous neutral delay differential equations using the variation of parameters method. These periodic solutions are expressed analytically. Two examples demonstrating the applicability of our results are also included. Second, we investigate the asymptotic behavior and estimation of solutions to linear nonhomogeneous neutral delay differential equations. The results are obtained using an appropriate real root of the relevant characteristic equation. Three examples are given to illustrate our results. Finally, we present the special case of first-order linear nonhomogeneous neutral delay differential equations with constant coefficients and constant delays, and provide an interesting example.