【摘要】 研究了定义在[0,1]区间且在点t0∈(0,1)具有界面条件的Sturm-Liouville算子的特征值与定义在子区间[0,t0]与[t0,1]上的两个Sturum-Liouville算子的特征值分布及其逆特征值问题.利用Weyl-Titchmarsh-m-函数的单调性态,证明了这三组谱之间具有交错性关系,并证明了若子区间上的两组谱不相交,则可由这三组谱唯一确定势函数q(x)与边值条件中的参数h和H.更多还原

【Abstract】 The eigenvalue and the inverse eigenvalue problems of the Sturm-Liouville operators defined respectively on[0,1][0,t0]and[t0,1]are considered.By using the monotonicity of the Weyl-Titchmarsh-m-function,it is shown that the three spectra are alternate,and the potential q(x)and the parameters h,Hin the boundary conditions can be uniquely determined by the three spectra if the spectra of the operators defined on subintervals are disjoint.更多还原