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

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].