Stability of Solutions of a System of first Order Ordinary Differential Equations with Finite Delay

Abstract

This thesis is concerned with the stability of solutions of a system of or- dinary di erential equations with nite delay. Fixed point theory is used in this thesis as the main mathematical tool to investigate the stability of solutions of a system of ordinary di erential equations with nite delay. In particular, the Banach xed point theorem is used. In the process the system of equations are inverted to obtain an equivalent integral equation. The result of the inversion is used to de ne a suitable mapping which is then used to derive the stability properties of the zero solution of the sys- tem of ordinary di erential equations with nite delay. Su cient conditions that guarantee that the zero solutions of a system of ordinary di erential equations with nite delay is asymptotically stable are obtained.