Initial Value Problems for Second Order Neutral Impulsive Integro-differential Equations with Advanced Argument

This paper discusses initial value problems for second order neutral impulsive integro-differential equations with advanced argument. By using the fixed point theorem of either Leray-Schaude or Banach, two existence results are obtained. By comparison, each of them has his own strong and weak points. If appropriate changes are made to some conditions for two results, the same results can be got. Two examples to illustrate our main results are given, which are compared with the existence results for impulsive differential equations from existing literature.