Electron. J. Differential Equations, Vol. 2017 (2017), No. 127, pp. 1-27.

Eigenvalues of Sturm-Liouville problems with discontinuous boundary conditions

Aiping Wang, Anton Zettl

Abstract:
For classical regular two-point self-adjoint Sturm-Liouville problems (SLP) the dependence of the eigenvalues on the boundary conditions is well understood because of some surprisingly recent results. Recently there has been a lot of interest in problems with discontinuous boundary conditions. Such conditions are known by various names including transmission conditions, interface conditions, point interactions (in the physics literature), etc. Here we extend the known classical results to such problems.

Submitted March 31, 2017. Published May 10, 2017.
Math Subject Classifications: 34B20, 34B24, 47B25.
Key Words: Eigenvalue properties; discontinuous boundary conditions.

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Aiping Wang
Department of Mathematics
Harbin Institute of Technology
Harbin 150001, China
email: aiping@hit.edu.cn
Anton Zettl
Mathematics Deparment
Northern Illinois University
DeKalb, IL, USA
email: zettl@msn.com

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