Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 661-670.

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A Class of Differential Operators with Eigenparameter Dependent Boundary Conditions

Kang Sun,Yunlan Gao*()   

  1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051
  • Received:2021-05-20 Online:2022-06-26 Published:2022-05-09
  • Contact: Yunlan Gao
  • Supported by:
    the NSFC(11661059);the NSF of Inner Mongolia(2017MS(LH)0103)


In this paper, A class of third-order differential operators with transition conditions and two boundary conditions containing spectral parameters is studied, and the analytical method is used to do two aspects of work. First, by constructing a new space and a new operator, the eigenvalues of the problem and the operator are connected so that the eigenvalues of the original problem are consistent with the eigenvalues of the new operator. Second, the properties of the eigenvalues of the original problem are studied, and the conclusion that the spectrum of the original problem has only point spectrum is given.

Key words: Differential operator, Boundary condition, Transition condition, Eigenvalues

CLC Number: 

  • O175