THE BASIS PROPERTY OF WEAK EIGENFUNCTIONS FOR STURM-LIOUVILLE PROBLEM WITH BOUNDARY CONDITIONS DEPENDENT RATIONALLY ON THE EIGENPARAMETER

Zhiyu Li; Zhaowen Zheng; Jianfang Qin

doi:10.11948/20230262

2024 Volume 14 Issue 1

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Zhiyu Li, Zhaowen Zheng, Jianfang Qin. THE BASIS PROPERTY OF WEAK EIGENFUNCTIONS FOR STURM-LIOUVILLE PROBLEM WITH BOUNDARY CONDITIONS DEPENDENT RATIONALLY ON THE EIGENPARAMETER[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 424-435. doi: 10.11948/20230262

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Zhiyu Li, Zhaowen Zheng, Jianfang Qin. THE BASIS PROPERTY OF WEAK EIGENFUNCTIONS FOR STURM-LIOUVILLE PROBLEM WITH BOUNDARY CONDITIONS DEPENDENT RATIONALLY ON THE EIGENPARAMETER[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 424-435. doi: 10.11948/20230262

THE BASIS PROPERTY OF WEAK EIGENFUNCTIONS FOR STURM-LIOUVILLE PROBLEM WITH BOUNDARY CONDITIONS DEPENDENT RATIONALLY ON THE EIGENPARAMETER

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
2.
College of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China

Author Bio: Email: 17860733868@163.com(Z. Li); Email: 764601129@qq.com(J. Qin)
Corresponding author: Email: zhwzheng@126.com(Z. Zheng)
Fund Project: The authors were supported by National Science Foundation of Shandong Province (Nos. ZR2023MA023, ZR2021MA047), Guandong Provincial Featured Innovation Projects of High School (No. 2023KTSCX067) and Graduate thesis research innovation funding (No. LWCXS202213)

Abstract

Abstract

Using the theory of operator pencils in Hilbert space and suitable integral transformation, the basis property of weak eigenfunctions for the Sturm-Liouville problem with eigenparameter dependent rationally on the boundary conditions is obtained, and the asymptotic behavior of eigenvalues is also involved.
- Sturm-Liouville problem /
- Riesz basis /
- eigenparameter-dependent boundary condition /
- weak eigenfunction
MSC: 47E05, 34B20, 34L10

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References

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