一类不连续奇异Strum-Liouville算子的渐近估计(英文)  

Asymptotic Behaviors of a Discontinuous Singular Sturm-Liouville Problem

作　　者：周立广[1,2] 王万义[1] 索建青[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021 [2]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《应用数学》2014年第1期107-117,共11页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundational of China(10961019,11361039)

摘　　要：本文考虑有限区间内一类边界条件含特征参数且在有限个内点处具有转移条件的奇异Strum-Liouville问题.通过定义一个适当的Hilbert空间,将所研究的Strum-Liouville转化成相应的自伴算子问题,因此,Strum-Liouville算子的特征值问题转化成了相应的自伴算子的特征值问题.进而,给出该问题特征值的相关性质并给出其渐近公式.A class of discontinuous singular Sturm-Liouville problems with eigenparameter dependent boundary conditions and with transmission conditions at inner points of considered finite interval is investigated. We definite a suitable Hilbert space and get a self-adjoint linear operator in this space in such a way that the considered problem can be interpreted as the eigenvalue problem of the new operator. Some properties and asymptotic formulas of the eigenvalues and fundamental solutions of the considered problem are investigated.

关 键 词：Strum—Liouville问题 特征参数 转移条件 渐近公式 

分 类 号：O175.3[理学—数学]