GREEN FUNCTION OF A CLASS OF EIGENPARAMETER DEPENDENT THIRD-ORDER DIFFERENTIAL OPERATORS WITH DISCONTINUITY

Yulin Bai; Wanyi Wang; Kun Li

doi:10.11948/20220529

2024 Volume 14 Issue 1

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Yulin Bai, Wanyi Wang, Kun Li. GREEN FUNCTION OF A CLASS OF EIGENPARAMETER DEPENDENT THIRD-ORDER DIFFERENTIAL OPERATORS WITH DISCONTINUITY[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 42-60. doi: 10.11948/20220529

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Yulin Bai, Wanyi Wang, Kun Li. GREEN FUNCTION OF A CLASS OF EIGENPARAMETER DEPENDENT THIRD-ORDER DIFFERENTIAL OPERATORS WITH DISCONTINUITY[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 42-60. doi: 10.11948/20220529

GREEN FUNCTION OF A CLASS OF EIGENPARAMETER DEPENDENT THIRD-ORDER DIFFERENTIAL OPERATORS WITH DISCONTINUITY

1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot, China
2.
Inner Mongolia Agricultural University, Hohhot, China
3.
School of Mathematical Sciences, Qufu Normal University, Qufu, China

Author Bio: Email: yulin@imnu.edu.cn(Y. Bai); Email: wwy@imu.edu.cn(W. Wang)
Corresponding author: Email: qslikun@163.com(K. Li)

Abstract

Abstract

This paper is concerned with a class of third-order boundary value problems with discontinuity, and the eigenparameter is contained in two of boundary conditions, the transmission conditions are imposed on the discontinuous point. Using operator theoretic formulation, we transfer the considered problem to a new operator $ \mathrm{T}$ in a modified Hilbert space $\mathcal{H}$. It is proved that $\mathrm{T}$ is a self-adjoint operator in $\mathcal{H}$, and we introduce some properties of the spectrum. The Green function and the resolvent operator are obtained. The completeness of eigenfunctions is also proved.
- Third-order differential operators /
- eigenparameter dependent boundary conditions /
- transmission conditions /
- Green function /
- completeness
MSC: 34B24, 34L15, 34L10

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References

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