Electron. J. Diff. Equ., Vol. 2013 (2013), No. 76, pp. 1-13.

Green's function for two-interval Sturm-Liouville problems

Aiping Wang, Anton Zettl

We construct the Green's function and the characteristic function for two-interval regular Sturm-Liouville problems with separated and coupled, self-adjoint and non-self-adjoint, boundary conditions. In the self-adjoint case these problems may have boundary conditions requiring jump discontinuities of the eigenfunctions or their derivatives. Such conditions are known by various names including transmission and interface conditions and have been studied by many authors in the recent literature.

Submitted March 3, 2013. Published March 18, 2013.
Math Subject Classifications: 34B20, 34B24, 47B25.
Key Words: Two-interval problems; Green's function; characteristic function.

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Aiping Wang
Mathematics Department
Harbin Institute of Technology
Harbin, 150001, China
email: wapxf@163.com
Anton Zettl
Mathematics Deparment
Northern Illinois University
DeKalb, IL 60115, USA
email: zettl@math.niu.edu

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