Fixed points and stability in nonlinear neutral Volterra integro-differential equations with variable delays

摘要

In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improve and extend the results in the literature. Two examples are also given to illustrate this work.