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

摘要

In this paper we use fixed point techniques to obtain asymptotic stability re- sults of the zero solution of a nonlinear neutral di.erential equation with variable delays. This investigation uses new conditions which allow the coe.cient functions to change sign and do not require the boundedness of delays. An asymptotic stability theorem with a necessary and su.- cient condition is proved. The obtained results improve and extend those due to Burton, Zhang, Ra.oul, Jin and Luo, Ardjouni and Djoudi, and Djoudi and Khemis. Two examples are also given to illustrate this work.