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

Abstract

Abstract: 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 containingeigenparameters. 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.

Key words: third-order differential operator, transmission condition, self-adjointness, dependence of eigenvalue

CLC Number:

O175

LIN Qiu-hong, QIAN Zhi-xiang. The self-adjointness and dependence of eigenvalues of third-order differential operator with eigenparameters in the boundary conditions[J]. Journal of Lanzhou University of Technology, 2023, 49(6): 160-168.

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