具有周期系数的左定Sturm-Liouville问题的特征值不等式  

Inequalities Among Eigenvalues of Left-Definite Sturm-Liouville Problems with Periodic Coefficients

作　　者：孙龙洁 郝晓玲[1] 牛天 Sun Longjie;Hao Xiaoling;Niu Tian(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《数学物理学报（A辑）》2020年第2期340-351,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561050);内蒙古自然科学基金(2018MS01021)。

摘　　要：该文利用了左定问题与右定问题的联系,得到了具有周期系数的左定Sturm-Liouville问题在区间[a,a+kh]上的周期和半周期特征值的描述,阐明了周期特征值之间的不等式关系,并明确给出了区间[a,a+kh]上的周期、半周期特征值和区间[a,a+h]上特征值的一一对应关系.In this paper,by using the relation between left-definite and right-definite problems,the characterization of the periodic and semi-periodic eigenvalues of left-definite Sturm-Liouville problems with periodic coeficients on the interval[a,a+kh]are obtained.For each k>2 we identify explicitly which of the uncountable number of complex conditions generates these periodic eigenvalues.Based on this condition,we give the inequality relation of periodic eigenvalues on the interval[a,a+kh]and 1-1 correspondence between the periodic and semi-periodic eigenvalues on the interval[a,a+kh],k>1 and the corresponding eigenvalues from the interval[a,a+h].

关 键 词：左定Sturm-Liouville问题 周期系数 特征值不等式 一一对应关系 

分 类 号：O175.9[理学—数学]