Sturm-Liouville问题的特征值与特征函数的渐近公式  

Asymptotic formula for eigenvalues and eigenfunctions of Sturm-Liouville question

作　　者：冉茂军 高承华 RAN Mao-jun;GAO Cheng-hua(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第2期57-62,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11961060);甘肃省自然科学基金资助项目(18JR3RA084).

摘　　要：根据经典的分析方法,研究了边界条件依赖非线性特征参数的四阶Sturm-Liouville问题的特征值与特征函数的渐近公式。通过常微分方程的常数变易法及特征函数零点渐近估计,获得了边界条件含有非线性特征参数的特征值与特征函数的渐近公式。According to the classical analysis method,the asymptotic formula of eigenvalues and eigenfunctions of Sturm-Liouville question with boundary conditions dependent on nonlinear eigenparameters are studied.By means of constant variation method of ordinary differential equation and asymptotic estimation of eigenfunction zero,the asymptotic formula of eigenvalues and eigenfunctions of boundary conditions with nonlinear eigenparameters are obtained.

关 键 词：STURM-LIOUVILLE问题 边界条件依赖特征参数 渐近公式 

分 类 号：O175.8[理学—数学]