向量半线性二阶脉冲泛函微分包含的C^1-可解性  

C^1-Solvability Criteria for Vector Semilinear Second-Order Impulsive Functional Differential Inclusions

作　　者：肖建中[1] 王智勇[1] 居加敏 XIAO JIANZHONG;WANG ZHIYONG;JU JIAMIN(School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《应用数学学报》2017年第6期820-840,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11571176;111701289)资助项目

摘　　要：本文在可分Banarch空间上研究了一类具局部条件与多值脉冲特征的二阶半线性中立型泛函微分包含,利用算子分裂方法、算子的余弦族理论及关于多值映射的Dhage不动点定理,分别给出当微分包含的多值非线性项是全连续映射与Lipschitz连续映射时C1-解的两个存在性定理,去掉了以往相关结果中关于余弦族的多余的紧性限制·A semilinear second-order neutral functional differential inclusion with nontocal conditions and multivalued impulse characteristics in a separable Banach space is considered. Two existence theorems for Cl-solutions are given, when the multivalued nonlinearity of the inclusion is a Lipschitz continuous map and a completely continuous map, respectively. The results are obtained by using operator splitting method, the theory of continuous cosine families of bounded linear operators and the fixed point theorem for multivalued maps due to Dhage. The crucial compactness restriction on the cosine family is removed from previous results.

关 键 词：脉冲泛函包含 算子的余弦族 多值映射的不动点 非紧性测度 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]