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A singular Sturm–Liouville problem with limit circle endpoint and boundary conditions rationally dependent on the eigenparameter

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Abstract

In this paper, a class of discontinuous singular Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter is considered. We define the operator formulation and give the properties of eigenvalues. Moreover, the completeness of its eigenfunctions is also discussed.

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Acknowledgements

The authors sincerely thank the referees for a number of constructive suggestions and corrections which have significantly improved the contents and the exposition of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Jinming Cai, Kun Li & Zhaowen Zheng

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  1. Jinming Cai
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  2. Kun Li
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  3. Zhaowen Zheng
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Correspondence to Zhaowen Zheng.

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This work was completed with Supported by the NSF of Shandong Province (nos. ZR2019MA034, ZR2020QA009 and ZR2020QA010) and Postdoctoral Foundation of China (2020M682139)

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Cai, J., Li, K. & Zheng, Z. A singular Sturm–Liouville problem with limit circle endpoint and boundary conditions rationally dependent on the eigenparameter. Mediterr. J. Math. 19, 184 (2022). https://doi.org/10.1007/s00009-022-02109-z

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  • DOI: https://doi.org/10.1007/s00009-022-02109-z

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