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.