矩阵值Sturm-Liouville问题解的渐近式及其应用  

Asymptotic solution of Sturm-Liouville problem with matrix values and its application

作　　者：陈素君 CHEN Su-jun(Department of Basic Courses,Guangdong Polytechnic College,Zhaoqing 526100,Guangdong,China)

机构地区：[1]广东理工学院基础课教学研究部,广东肇庆526100

出　　处：《西北师范大学学报（自然科学版）》2024年第5期110-119,共10页Journal of Northwest Normal University(Natural Science)

基　　金：广东省普通高校特色创新项目(自然科学)(2023KTSCX198)。

摘　　要：研究矩阵值Sturm-Liouville问题解的渐近式及其应用.首先,利用常数变易法,得到了关于矩阵值Sturm-Liouville问题解的渐近式;然后,让其系数满足一定的条件,利用逐步迭代法得到了解的精确渐近式,并且给出了渐近式的性质;最后,应用解的渐近式研究了矩阵值Sturm-Liouville微分算式的亏指数,并利用亏指数理论定量分析了Sturm-Liouville算子谱的分布.The asymptotic solution of Sturm-Liouville(S-L)problem with matrix values and its application are studied.Firstly,the asymptotic solution of the S-L problem with matrix values is obtained by using the method of constant variation.Then,let the coefficient meet certain conditions,the exact asymptotic solution is obtained by using the stepwise iterative method,and the asymptotic properties of the solution are also given.Finally,the deficiency index of the matrix value S-L differential expression is discussed by using the asymptotic solution,and the spectrum distribution of S-L operators is analyzed quantitatively by using the deficiency index theory.

关 键 词：解的渐近式 亏指数 J-自伴微分算子 谱核 离散谱 本质谱 

分 类 号：O175.3[理学—数学]