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

Based on the semigroups of linear operators theory, the paper discussed the existence of mild solutions and uniqueness of classical solutions to the initial value problems for nonlinear impulsive evolution equationsin Banach spaces on infinite interval and the main results are as follows:1.The impulsive functions not using any extra conditions and the semigroups being analytic or compact, the author obtains the existence results of mild solutions and uniqueness of classical solutions by the method of extending interval by interval on infinite interval.2.The impulsive functions using very few conditions or not using any extra conditions and the semigroups being positive, the author discusses the existence results of mild solutions on finite or infinite interval by using the monotone iterative method .3.Applications to the initial value problems for the impulsive parabolic partial differential equations,the author obtains the existence results of classical solutions.