ASYMPTOTIC STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

Abstract

In this paper, we study the asymptotic stability of a generalized nonlinear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton <cite>b5</cite>, Zhang <cite>z</cite>, Dib, Maroun and Raffoul <cite>d1</cite>, and Ardjouni and Djoudi <cite>a2.1</cite>. An example is also given to illustrate our results.