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A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition

Author

Listed:
  • Jinming Cai

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Zhaowen Zheng

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Kun Li

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using an operator-theoretical formulation, we transfer the problem to an operator in an appropriate Hilbert space. It is proved that the operator is self-adjoint. We also give the asymptotic formulas of the eigenvalues of the problem. Moreover, Green’s function is also discussed.

Suggested Citation

  • Jinming Cai & Zhaowen Zheng & Kun Li, 2022. "A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4430-:d:982690
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