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Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

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Abstract

In this study, we consider the singular Sturm-Liouville (S-L) problem with transmission conditions (TC). The eigenvalues of the singular S-L problem with TC are investigated. By defining a new Hilbert space which is related to TC, the self-adjointness of the S-L problem in this associated Hilbert space is proved. And we give the condition for \(\lambda \) being the eigenvalue of the singular S-L problem. Furthermore, the asymptotic behavior of eigenvalues of the singular S-L problem is described.

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Acknowledgements

The authors thank the reviewer for the careful reading of the paper and for the constructive comments. This work is supported by National Natural Science Foundation of China (11761030, 11661059) and Natural Science Foundation of Hubei Province (2017CFB352).

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Authors and Affiliations

  1. School of Science, Hubei University for Nationalities, Enshi, 445000, China

    Dan Mu

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

    Ji-jun Ao

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  1. Dan Mu
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  2. Ji-jun Ao
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Correspondence to Dan Mu.

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Mu, D., Ao, Jj. Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions. Differ Equ Dyn Syst 31, 17–29 (2023). https://doi.org/10.1007/s12591-020-00520-0

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