带谱参数边界条件的二维向量型Sturm-Liouville问题特征值的依赖性  

Dependence of eigenvalues of two-dimensional vector Sturm-Liouville problems with eigenparameter dependent boundary conditions

作　　者：张岚芳 敖继军[1] 韩仪鹏 ZHANG Lanfang;AO Jijun;HAN Yipeng(School of Science,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《内蒙古工业大学学报（自然科学版）》2024年第4期289-295,共7页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金项目(12261066,11661059);内蒙古自治区自然科学基金项目(2021MS01020)。

摘　　要：研究一类定义在区间[a,b]上的二维向量型Sturm-Liouville问题,通过构造适当的内积与Hilbert空间给出算子自伴性的证明。研究了该问题特征值与特征函数的依赖性问题,主要讨论特征值的连续性及其对各参数的可微性,并给出特征值对各个参数的微分表达式。Two-dimensional vector Sturm-Liouville problems defined on interval[ab]are investigated.By constructing a suitable inner product and Hilbert space,the self-adjointness of the operator is proved.Next,the dependence of the eigenvalues and the eigenfunctions of the problems is studied,focusing primarily on the continuity of the eigenvalues and their differentiability with respect to various parameters.Moreover,differential expressions for the eigenvalues with respect to each parameter are provided.

关 键 词：向量型Sturm-Liouville问题 带谱参数的边界条件 连续性 可微性 

分 类 号：O175.3[理学—数学]