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Dependence of Eigenvalues of Sturm–Liouville Problems with Eigenparameter-Dependent Boundary Conditions and Interface Conditions

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Abstract

In this paper, regular Sturm–Liouville problems with eigenparameter-dependent boundary conditions and interface conditions are investigated. We obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problem: the coefficients, the boundary conditions, the interface conditions, as well as the endpoints. Moreover, we find the differential expressions for each parameters, respectively.

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Acknowledgements

The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. This work is supported by National Natural Science Foundation of China (Grant No. 11661059) and Natural Science Foundation of Inner Mongolia (Grant Nos. 2021MS01020 and 2017JQ07).

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Authors and Affiliations

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

    Hai-Yan Zhang, Ji-jun Ao & Meng-lei Li

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  1. Hai-Yan Zhang
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  2. Ji-jun Ao
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  3. Meng-lei Li
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Correspondence to Ji-jun Ao.

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Zhang, HY., Ao, Jj. & Li, Ml. Dependence of Eigenvalues of Sturm–Liouville Problems with Eigenparameter-Dependent Boundary Conditions and Interface Conditions. Mediterr. J. Math. 19, 90 (2022). https://doi.org/10.1007/s00009-021-01943-x

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  • DOI: https://doi.org/10.1007/s00009-021-01943-x

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