Stability of totally nonlinear neutral differential Equations with multiple time-varying delays

Abstract

This thesis is concerned with the stability properties of solutions of nonlinear neutral differential equations with multiple time varying delays. Fixed point theory is used in this thesis to investigate the stability properties of solutions of nonlinear neutral differential equations with multiple time varying delays. In particular, the contraction mapping principle is used in this thesis. The nonlinear neutral differential equation is inverted to obtain an equivalent integral equation. The result of the inversion is used to define a suitable mapping which is then used to discuss the stability properties of solutions of nonlinear neutral differential equations with multiple time varying delays. Sufficient conditions that guarantee that the zero solutions of nonlinear neutral differential equations with multiple time varying delays are asymptotically stable are derived.