解一类抽象积-微分方程的积分半群方法  

INTEGRETED SEMIGEOUP METHODS TO SOLVE A CLASS OF ABSTRACT INTEGRODIFFERENTIAL EQUATIONS

作　　者：孙仁康[1] 刘清荣[1] 

机构地区：[1]西北大学数学系

出　　处：《纯粹数学与应用数学》1993年第1期95-99,共5页Pure and Applied Mathematics

摘　　要：在这篇文章内,研究一类含参数线性算子族A(t)和线性算子B的积-微分方程,应用积分半群方法证明了该方程存在指数有界解,和含A(t),B的二阶微分方程存在指数有界积分解。这里A(t),B不必满足Hille-Yosida条件。In this paper a class of abstract integrodifferential equations with linear op-erator family A(t) and linear operater B in Banach space are studied. Using integratedsemigroup methods proved that a class of abstract integrodifferential equations and inte-gral equations exist exponentially bounded solutions, and that second order differentialequations and Cauchy problems exist exponentially bouded integrated solutions. Thoseequations include A(t) and B which not necessarily satisfy the Hille-Yosida condition andthe density of domain, but B generate integrated semigroup.

关 键 词：积分半群 积分微分方程 C0半群 线性算子 

分 类 号：O175.6[理学—数学]