On Some Qualitative Properties of Solutions For Higher Order Neutral Differential Equations

Abstract

This thesis investigates asymptotic, uniform, and exponential stability, as well as boundedness and square integrability of solutions to certain higher-order nonlinear neutral delay differential equations. Serval analytical techniques are employed, chiefly Lyapunov’s second (direct) method, based on constructing candidate Lyapunov functionals. We derive new sufficient conditions that improve and extend many published results. Finally, several illustrative (and numerical) examples are presented to demonstrate the validity of the theoretical findings. These contributions enhance the understanding of neutral delay differential equations and provide a mathematical basis for future studies of more complex systems with multiple delays and/or time-varying coefficients.