• 论文 •

### 边界条件含有特征参数的四阶微分算子的自伴性和特征值的依赖性

1. 内蒙古工业大学理学院 呼和浩特 010051
• 收稿日期:2021-08-12 出版日期:2022-06-26 发布日期:2022-05-09
• 通讯作者: 许美珍 E-mail:xumeizhen1969@163.com
• 基金资助:
国家自然科学基金(11561051);内蒙古自然科学基金(2021MS01020)

### The Self-Adjointness and Dependence of Eigenvalues of Fourth-Order Differential Operator with Eigenparameters in the Boundary Conditions

Wenwen Yan,Meizhen Xu*()

1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051
• Received:2021-08-12 Online:2022-06-26 Published:2022-05-09
• Contact: Meizhen Xu E-mail:xumeizhen1969@163.com
• Supported by:
the NSFC(11561051);the NSF of Inner Mongolia(2021MS01020)

Abstract:

In this paper we consider the self-adjointness and the dependence of eigenvalues of a class of discontinuous fourth-order differential operator with eigenparameters in the boundary conditions of one endpoint. By constructing a linear operator T associated with problem in a suitable Hilbert space, the study of the above problem is transformed into the research of the operator in this space, and the self-adjointness of this operator T is proved. In addition, on the basis of the self-adjointness of the operator T, we show that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem, and give the corresponding differential expressions. In particular, giving the Fréchet derivative of the eigenvalue with respect to the eigenparameter-dependent boundary condition coefficient matrix, and the first-order derivatives of the eigenvalue with respect to the left and right sides of the inner discontinuity point c.

• O175.3