【摘要】 讨论了一类边条件含特征参数有理式的Sturm-Liouville问题的特征值不等式及其逆谱问题.利用Weyl-Titchmarsh m-函数的分段单调性,得到这类Sturm-Liouville问题的特征值与一类经典Sturm-Liouville问题的特征值,以及1个常数间的交替不等式,同时得到由含特征参数有理式的边条件和Dirichlet边条件确定的2个常微分算子的特征值可唯一确定势函数.更多还原

【Abstract】 The inequality among eigenvalues and inverse eigenvalue problem of a class of Sturm-Liouville problem with rational expression of eigenparameter in boundary conditions are discussed. Using the piecewise monotonic of Weyl-Titchmarsh m-function of Sturm-Liouville problem, we obtain that the inequalities among the eigenvalues of Sturm-Liouville problems with rational expression of eigenparameter in the boundary conditions and the eigenvalues of a classical Sturm-Liouville problem with Dirichlet boundary conditions and a constant. We also show that the potential can be determined by the set of eigenvalues of the Sturm-Liouville problems with rational expression of eigenparameter in boundary conditions and Dirichlet boundary conditions.更多还原