二阶非线性积微分方程的温和解的存在性  

The existence of mild solution for second order nonlinear integro-differential equations

作　　者：周爱仁[1] 彭云飞[1] 

机构地区：[1]贵州大学理学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2007年第3期62-65,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：贵州省省长基金

摘　　要：考虑在无穷维Banach空间中,受无界算子扰动的二阶非线性积微分方程。首先构造由算子矩阵生成的半群,引进合理的温和解,并证明了二阶积微分方程的温和解的存在唯一性和解对初值的连续依赖性。In this paper,the second order nonlinear integro-differential equations perturbed by unbounded operator on infinite dimensional Banach spaces is considered.The semigroup generated by operator matrix is constructed.Introducing the reasonable mild solution for second order nonlinear integro-differential equations,the existence uniqueness of mild solutions and continuous dependence of the solutions on the initial data are proved.

关 键 词：无界算子矩阵 二阶方程 积分算子 存在性 温和解 

分 类 号：O175.6[理学—数学] O177.1[理学—基础数学]