Banach空间上一类算子微分系统解的存在性与唯一性  

Existence and uniqueness of solutions of an operator-differential system in Banach space

作　　者：贾云锋[1] 薛盼[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2013年第2期5-8,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11001160);中央高校基本科研业务费专项资金项目(GK201002046)

摘　　要：运用强连续余弦算子族理论、压缩映像原理以及Gronwall-Bellman型积分不等式,研究了建立在Banach空间上一类二阶半线性非齐次算子微分系统解的存在性等性质.研究结果表明:在一定条件下系统存在唯一解并且解对初值具有连续依赖性;同时还证明了解的有界性,并对解进行了估计.By using the theory of the strongly continuous cosine family, the principle of properties of solutions of a second order semi-linear and nonhomogeneous operator-differential system in a Banach space are investigated. It is proved that the system has a unique solution and it continuously depends on the initial values under certain conditions; furthermore, the boundedness and the prior estimation on the solution are also presented.

关 键 词：算子微分系统 解 存在性 唯一性 LIPSCHITZ条件 

分 类 号：O177.2[理学—数学] O175.6[理学—基础数学]