Study On The Existence Of Solutions For Second-order Impulsive Differential Equations

This paper is on the existence of solutions for second-order impulsive differential equations,including four chapters.The main results are in chapter 3 and chapter 4.In chapter 3,a fixed point analysis approach is used to investigate the existence of mild solutions of second order semi-linear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the co-sine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,as a special example,we study a equation’s existence,which is with impulsive and delay.In chapter 4,it is concerned with the controllability of second order impulsive functional differential systems with infinite delay in Banach spaces.Sufficient condi-tions are formulated and proved for the exact controllability of such systems,without imposing a compactness condition on semigroup of cosine family,by using a fixed point analysis approach.Finally,an example is presented to illustrate the theory.