Methods and Applications of Analysis

Volume 22 (2015)

Number 1

Self-adjoint Sturm-Liouville problems with discontinuous boundary conditions

Pages: 37 – 66



Aiping Wang (Department of Mathematics, Harbin Institute of Technology, Harbin, China)

Anton Zettl (Department of Mathematics, Northern Illinois University, DeKalb, Illinois, U.S.A.)


We present a general framework for the study of self-adjoint Sturm-Liouville problems with discontinuous boundary conditions specified at interior points of the underlying interval. Some regular such conditions have been studied and are known by various names including transmission conditions, interface conditions, multi-point conditions, point interactions (in the Physics literature) etc. Using this framework we generate additional regular conditions and singular analogues of all these regular conditions. In the singular case the solutions and their (quasi) derivatives may have finite as well as infinite jump discontinuities.


self-adjoint domains, transmission and interface conditions, point interactions

2010 Mathematics Subject Classification

Primary 34B20, 34B24. Secondary 47B25.

Published 1 April 2015