一类四阶边值问题的特征值对边界的依赖性（英文）  

Dependence of Eigenvalues of a Class of Fourth-order Boundary Value Problems on the Boundary

作　　者：葛素琴[1] 王万义[2] 刘忻梅[1] 

机构地区：[1]内蒙古科技大学理学院,内蒙古包头014010 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2016年第3期554-562,共9页Mathematica Applicata

基　　金：Supported by the National Nature Science Foundation of China(11361039);the innovation fund of Inner Mongolia University of Science and Technology(2015QDL19)

摘　　要：本文研究四阶边值问题的特征值对边界的依赖性问题,指出带有支撑边界条件的四阶边值问题的特征值连续且光滑地依赖于边界点,给出其第n个特征值关于一端点的一阶微分表达式,并证明当区间长度趋于零时,其所有的特征值会趋于无穷.In this paper we study the dependence of eigenvalues of fourth-order boundary value problems on the boundary. We show that the eigenvalues of fourth-order boundary value problems with supported ends depend not only continuously but smoothly on boundary points, and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks to zero all higher eigenvalues march off to plus infinity.

关 键 词：四阶边值问题 特征值 特征函数 依赖性 

分 类 号：O175.3[理学—数学]