一类边界条件含谱参数的微分算子

A Class of Differential Operators with Eigenparameter Dependent Boundary Conditions

该文考虑了一类具有转移条件且两个边界条件含谱参数的三阶微分算子,利用分析法做了两方面的工作,一是通过构造新空间和新算子将所考虑问题的特征值与新算子的特征值建立联系,使原问题的特征值和新算子的特征值一致.二是研究了原问题的特征值的性质,且给出了原问题的谱只有点谱的结论.

In this paper,A class of third-order differential operators with transition conditions and two boundary conditions containing spectral parameters is studied,and the analytical method is used to do two aspects of work.First,by constructing a new space and a new operator,the eigenvalues of the problem and the operator are connected so that the eigenvalues of the original problem are consistent with the eigenvalues of the new operator.Second,the properties of the eigenvalues of the original problem are studied,and the conclusion that the spectrum of the original problem has only point spectrum is given.