Stability of a Completely Delayed Dynamic Equation on Time Scale with Variable Delays

Abstract

This thesis is about the stability of completely delayed dynamic equations on time scale. Fixed point theory is used to study the stability properties of the zero solution of dynamic equations on time scales. In particular, the Banach xed point theorem is used in this thesis.The dynamic equation is inverted into an equivalent integral dynamic equation and a suitable de ne map- ping is de ned based on the equivalent integral dynamic equation which is then used to discuss the stability properties of the zero solution of the dynamic equation. Su cient conditions are obtained for the zero solution of completely delayed dynamic equations to be asymptotically stable.