Fixed point techniques and stability in nonlinear neutral differential equations with variable delays

Abstract

In this paper we use fixed point techniques to obtain asymptotic stabilityresults of the zero solution of a nonlinear neutral differential equation withvariable delays. This investigation uses new conditions which allow thecoefficient functions to change sign and do not require the boundedness ofdelays. An asymptotic stability theorem with a necessary and sufficientcondition is proved. The obtained results improve and extend those due toBurton, Zhang, Raffoul, Jin and Luo, Ardjouni and Djoudi, and Djoudi and Khemis. Two examples arealso given to illustrate this work.