边条件含特征参数Sturm-Liouville问题的特征值不等式及逆问题  

Inequality and Inverse Problem of Eigenvalues for Sturm-Liouville Problem with Eigenparameters in the Boundary Conditions

作　　者：傅守忠[1] 王忠[1] 

机构地区：[1]肇庆学院数学与信息科学学院,广东肇庆526061

出　　处：《内蒙古大学学报（自然科学版）》2013年第6期561-564,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11171295和11171198)

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-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.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.

关 键 词：Sturm—Liouville问题 逆问题 特征值 

分 类 号：O175.3[理学—数学]