Dependence of Eigenvalues of Discontinuous Fourth-order Differential Operators with Eigenparameter Dependent Boundary Conditions

In this paper, we investigate a fourth-order differential operator with eigenparameter dependent boundary conditions and transmission conditions. To study the eigenvalues of the problem, we establish a new operator associated with the considered problem. Furthermore, we prove that the eigenvalues ar...

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Bibliographic Details
Published in:Journal of nonlinear mathematical physics 2022-12, Vol.29 (4), p.776-793
Main Authors: Qin, Jianfang, Li, Kun, Zheng, Zhaowen, Cai, Jinming
Format: Article
Language:English
Subjects:
Banach spaces
Boundary conditions
Boundary value problems
Differential equations
Eigenvalues
Hilbert space
Mathematical Physics
Mathematics
Mathematics and Statistics
Neighborhoods
Operators (mathematics)
Parameters
Partial differential equations
Research Article
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Summary:In this paper, we investigate a fourth-order differential operator with eigenparameter dependent boundary conditions and transmission conditions. To study the eigenvalues of the problem, we establish a new operator associated with the considered problem. Furthermore, we prove that the eigenvalues are differentiable depending on the parameters of the problem. Finally, the differential expressions of the eigenvalues with respect to all parameters are given.
ISSN:1776-0852
1402-9251
1776-0852
DOI:10.1007/s44198-022-00060-x