【摘要】 讨论一类边条件含特征参数的Sturm-Liouville问题的特征值不等式及逆谱问题.利用Weyl-Titchmarsh m-函数的分段单调性,得到边条件线性含特征参数的Sturm-Liouville问题的特征值与经典Sturm-Liouville问题的特征值及一个常数间的交替不等式.同时得到由含特征参数的边条件和Dirichlet边条件确定的两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 SturmLiouville problems with eigenparameters in boundary conditions are discussed.Using the piecewise monotonic of Weyl-Titchmarsh m-function,it is obtained that the inequalities among the eigenvalues of Sturm-Liouville problems with eigenparameter in the boundary conditions and the eigenvalues of a classical Sturm-Liouville problems with Dirichlet boundary conditions and a constant.It is also shown that the potential can be determined by the set of eigenvalues of Sturm-Liouville differential equation with eigenparameters in boundary conditions and Dirichlet boundary conditions.更多还原