耦合边界条件下Sturm-Liouville问题的渐近展开  

The Asymptotic Expansion of Sturm-Liouville Problem with Coupled Boundary Condition

作　　者：张晓军[1] 杨树生[1] 李珊珊[1] 贾利东[1] 杜永霞[1] 

机构地区：[1]河套学院理学系,内蒙古巴彦淖尔015000

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2016年第6期749-752,756,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：内蒙古自治区高等学校科学研究项目(NJZY259)

摘　　要：利用分析方法和矩阵方法,解决了利用Wronski行列式与Liouvill公式处理特征值与特征函数渐进展开时遇到的困难.在一般耦合边界条件{(y(b)(py′)(b))=e^(iθ)K(y(a)(py′)(a))下,满足条件k_(12)=k_(21)=0时,给出了所讨论问题的特征值与特征函数的渐近展开.The problems in dealing with the asymptotic expansion of eigenvalue and eigenfunetion by using Wronski det and Liouvill formula are solved through the combination of analytical and matrix methods. The eigenvalue of the problems discussed and the asymptotic expansion of eigenvalue and eigenfunction are offered under the coupled boundary condition {（y（b）（py′）（b））=e^iθK（y（a）（py′）（a）） in which a certain condition k12 =k21 =0 is satisfied.

关 键 词：CAUCHY PROBLEM 特征值 特征函数 耦合边界条件 渐近展开 

分 类 号：O175.3[理学—数学]