On the Behaviors of Solutions of Linear Nonhomogeneous Mixed Type Differential Equations

This paper deals with the behaviors of solutions for nonhomogeneous linear mixed-type (delay and advance) differential equations. In this study, an asymptotic result and a useful exponential estimate for the solutions are established. Additionally, stability criteria for the homogeneous equation are also obtained. We obtained these results using a real root (with a suitable property) of the characteristic equation. We present three examples to illustrate the hypotheses of these results. We also obtain useful lemmas that give sufficient conditions for the existence of the roots of the characteristic equation.