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

Jinming Cai (), Zhaowen Zheng and Kun Li
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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

Mathematics, 2022, vol. 10, issue 23, 1-17

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.

Keywords: singular Sturm–Liouville problem; transmission condition; eigenparameter-dependent boundary condition; asymptotic formula of an eigenvalue; Green’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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