一类具有转移条件的向量Sturm-Liouville问题的特征值  

Some Eigenvalue Problems for Vectorial Sturm-Liouville Equations with Transmission Conditions

作　　者：李春晨[1] 孙炯[1] 李昆[1] 郝晓玲[1] LI Chun-chen SUN Jiong LI Kun HAO Xiao-ling(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2017年第10期227-235,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11561050;11401325);高等学校博士学科点专项科研基金(新教师类)(20121501120003)

摘　　要：考虑了一类具有转移条件的向量Sturm-Liouville问题的特征值及其重数问题.首先构造了与问题相关的新内积和基本解,得到特征值的充要条件.在此基础上证明了二维情况下,问题特征值的代数重数与几何重数相等.In this paper, the eigenvalues and its multiplicity for a class of vectorial SturmLiouville equations with transmission conditions is considered. A new inner product asso- ciated with the problems and the fundamental solutions are constructed. Then we get the necessary and sufficient conditions for the eigenvalues, show that the algebraic multiplicity of eigenvalues of the two-dimensional problems is equal to its geometric multiplicity.

关 键 词：转移条件 向量Sturm—Liouville问题 特征值 几何重数 代数重数 

分 类 号：O183.1[理学—数学]