一类含特征参数依赖边界条件的不连续三阶微分算子

A class of discontinuous third-order differential operators with eigenparameter dependent boundary conditions

考虑一类具有转移条件且一个边界条件含谱参数的三阶微分算子,首先通过构造新空间和新算子,得到了原问题的特征值是实的的结论;其次得到原问题的特征值存在的充要条件,同时证明了原问题最多有可数个实的特征值,并且没有有限值的聚点;最后证明了原问题的谱只有点谱。

This paper deals with a class of third-order differential operators with transition conditions and two boundary conditions containing spectral parameters.Two important issues are discussed using analytical methods.The first is to construct a new space and a new operator to combine the eigenvalues of the problem under consideration,establishing a connection with the eigenvalues of the operator,so that the eigenvalues of the original problem are consistent with the eigenvalues of the new operator.The second is to study the properties of the eigenvalues of the original problem,and give the conclusion that the spectral of the original problem is only the point spectral.