Eigenvalues of fourth-order boundary value problems with distributional potentials

Hai-yan Zhang; Ji-jun Ao; Fang-zhen Bo; Hai-yan Zhang; Ji-jun Ao; Fang-zhen Bo

doi:10.3934/math.2022407

AIMS Mathematics

2022, Volume 7, Issue 5: 7294-7317. doi: 10.3934/math.2022407

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Research article

Eigenvalues of fourth-order boundary value problems with distributional potentials

1.
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
2.
Normal College, Hohhot Vocational College, Hohhot 010051, China

Received: 10 November 2021 Revised: 21 January 2022 Accepted: 29 January 2022 Published: 10 February 2022
MSC : 34B09, 34L10, 34B05, 47A75

This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.
- fourth-order boundary value problems,
- distributional potentials,
- quasi-derivatives,
- eigenvalues
Citation: Hai-yan Zhang, Ji-jun Ao, Fang-zhen Bo. Eigenvalues of fourth-order boundary value problems with distributional potentials[J]. AIMS Mathematics, 2022, 7(5): 7294-7317. doi: 10.3934/math.2022407

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Abstract

This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.

References

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