Existence Of Solutions For Second-order Impulsive Differential Inclusions

It’s an important and common method that studying the existence of solu-tions for impulsive differential inclusions by fixed points theorems.This thesis use fixed point theorems to research the existence of solutions for second-order im-pulsive semilinear differential inclusions under periodic boundary conditions and nonlocal initial value conditions.Our results generalize some known results.It is consists of three chapters,its main content is as follows:In Chapter 1,introduce the historical background of issues and the main works of this article.In Chapter 2,research the existence of solutions for second-order impulsive semilinear diferential inclusions under periodic boundary conditions.This chap-ter use nonlinear alternative fixed point theorem and contraction multi-valued operators fixed point theorem add cosine family theory of multi-valued analysis to discuss the existence of solutions under impulsive function respectively satisfy sublinear growth,lim|y|â†'∞Ik(y)y/=0 and Lipschitz conditions.In Chapter 3,research the existence of solutions for second-order impulsive semilinear differenti al inclusions under nonloc al conditions.By using semigroup theory,the measure of noncompactness theorems,multi-valued analysis knowledge and related to the fixed point theorem to discuss the existence of solutions under loss of compactness of semigroup conditions.