An analysis on the stability of a state dependent delay differential equation

Abstract

In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term τ(u(t)) = a+bu(t)/c+bu(t). Moreover, we put the some restrictions for the positivity of delay term τ(u(t)). Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.