边界条件含特征参数的三阶微分算子的自伴性和特征值的依赖性

The self-adjointness and dependence of eigenvalues of third-order differential operator with eigenparameters in the boundary conditions

研究一类边界条件含有特征参数且具有转移条件的三阶微分算子的自伴性和特征值的依赖性.通过在新的Hilbert空间定义线性算子T,将问题转化为对相关线性算子T的研究.利用算子理论,证明了该算子的自伴性,在此基础上,讨论了特征值的连续性,特别研究了特征值关于相关参数的可微性,并得到相应的微分表达式.

This paper deals with the self-adjointness and the dependence of eigenvalues of a class of third-order differential operators with transmission conditions and two boundary conditions containing eigenparameters.By defining linear operator in a new Hilbert space,the problem is transformed into the study of the corresponding linear operator.Using the operator theory,the self-adjointness of the operator is proved,and subsequently the continuity of eigenvalues is discussed.In particular,the differentiability of eigenvalues with respect to the related parameters is examined,and the corresponding differential expressions are derived.