【作者】 费明稳；

【导师】 孙国正；

【作者基本信息】 安徽师范大学 ， 基础数学， 2006， 硕士

【摘要】 本文共分三章。第一章首先证明了关于Hille-Yosida算子的两种无界扰动仍是Hille-Yosida算子的两个扰动定理，然后依此给出了边界扰动抽象边值问题的适定性的两种判别方法。第二章利用算子矩阵的分解分别给出了边界算子无界和有界两种情形下抽象动态边值问题解析性的判别方法。第三章利用算子矩阵和正半群的结果给出了抽象动态边值问题的正性和稳定性的等价刻画，推广了文[5]的结果，作为应用，讨论了时滞微分方程的正性和稳定性。更多还原

【Abstract】 This thesis is divided into three parts. In the first character,two theorems about the unbounded perturbation of Hille — Yosida operator are proved,and with them we give two results on how to characterise the wellposedness of abstract boundary value problem with boundary perturbation.In the second character,we characterise the analyticity of abstract dynamic boundary value problem with unbounded boundary operator and abstract dynamic boundary value problem with bounded boundary operator using the decomposition of operator matrices.In the last character,the necessary and sufficient conditions for the positivity and stability of abstract dynamic boundary value problem are presented,which generalise some results in [5].As application,we discuss the positivity and stability of differential equation with delay.更多还原