中文摘要：

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Sturm—Liouville问题的Weyl—Titchmarshm一函数的分段单调性，得到边条件线性含特征参数的Sturm—Liouville问题与经典Sturm—Liouville问题的特征值间的交替不等式．然后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的结论．

英文摘要：

The inequality among eigenvalues and inverse eigenvalue problem were discussed for a class of Sturm-Liouville problem with eigenparameter dependent boundary condition. By studying the piecewise monotonicity of Weyl-Titchmarsh rn -function of Sturm-Liouville problem,an inequali- ty among eigenvalues was obtained concerning the Sturm-Liouville problem with eigenparameter in the boundary conditions and eigenvalues of a classical Sturm-Liouville problem under Dirichlet boundary conditions. The inverse eigenvalue problem was studied, and the results showed that the potential can be determined by the set of eigenvalues for eigenparameters with linear dependent boundary conditions and Dirichlet boundary conditions.