Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 182, pp. 1-16.
Reconstructing the potential function for indefinite
Sturm-Liouville problems using infinite product forms
Mohammad Dehghan, Ali Asghar Jodayree
Abstract:
In this article we consider the linear second-order equation of
Sturm-Liouville type

where
is a real parameter,
is the potential function
and
is the weight function. We use the infinite product
representation of the derivative of the solution to the differential equation
with Dirichlet-Neumann conditions, and for the system of dual equations
which is needed for expressing inverse problem and for retrieving potential.
It must be mentioned that the weight function has a zero whose order
is an integer called a turning point.
Submitted July 15, 2013. Published August 7, 2013.
Math Subject Classifications: 34B24, 34A55, 34E20, 34E05.
Key Words: Indefinite Sturm-Liouville problem; turning point; dual equations;
infinite product form.
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Mohammad Dehghan
Faculty of Mathematical Sciences
University of Tabriz
Tabriz, Iran
email: m-dehghan@tabrizu.ac.ir, Tel. +989113512619
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Ali Asghar Jodayree
Faculty of Mathematical Sciences
University of Tabriz
Tabriz, Iran
email: akbarfam@yahoo.com
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