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 differential equations with finite 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 differential equations with finite delay. In particular, the Banach fixed 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 define a suitable mapping which is then used to derive the stability properties of the zero solution of the sys tem of ordinary differential equations with finite delay. Sufficient conditions that guarantee that the zero solutions of a system of ordinary differential equations with finite delay is asymptotically stable are obtained.