The Existence Of The Global Solutions To The Initial Value Problems For Impulsive Equations In Banach Space

Based on the fixed point theorem of condensing mapping .the partial order theory and the theorem about the existence of approximate solution , the paper discussed the existence and uniqueness of solutions to the initial value problems for nonlinear first-order impulsive differential equationsin Banach spaces and the main results are as follows:1.The impulsive functions not using compacting and any extra conditions, the author obtains the existence results of solutions by the method of extending interval by interval on infinite interval and essentially improves the results.2.Neither using noncompactness measure condition,nor assuming the existence of upper and lower solutions, the author discusses the existence and uniqueness results of positive solutions on infinite interval by using the monotone iterative method .In this process,the author improves the results without assumption of monotonicity on impulsive functions.3.Under the dissipative conditions, the uniqueness results of initial value problems for first-order impulsive equations are obtained by using the theorem about the existence of approximate solution on infinite interval.The main results of this paper show that nonimpulsive problems are essentially similar with the initial value problems for impulsive differentialequations in Banach spaces.Therefore ,only need we consider nonimpulsive problems.