Half inverse problem for singular differential operator

Abstract

A spectral analysis for the Sturm–Liouville equation defined on (0,1] and singularity of type

at zero is investigated (l is an integer). As known, the potential function q(x) in the singular Sturm–Liouville problem can be uniquely determined from two spectrum. In this study, we show that if q(x) is prescribed on (1/2,1], then only one spectrum is sufficient to determine q(x) on the interval (0,1/2).

Keywords:

• Spectrum
• Sturm–Liouville problem
• AMS(MOS) Subject Classifications: 34L05
• 34B24

Acknowledgement

The authors wish to express their thanks to Professor A. Hasanov for their suggestions in the preparation of this proof.