Inverse problems for the matrix Sturm–Liouville equation with a Bessel-type singularity

ABSTRACT

The matrix Sturm–Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. We consider inverse problems by the Weyl matrix and by the spectral data for this equation. Constructive solutions, based on the method of spectral mappings, are obtained for these inverse problems.

KEYWORDS:

• Matrix Sturm–Liouville equation
• Bessel-type type singularity
• inverse problem
• method of spectral mappings

AMS SUBJECT CLASSIFICATIONS:

• 34A55
• 34L40
• 34B09
• 47E05

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Russian Federation President [grant number MK-686.2017.1]; the Russian Ministry of Education and Science [grant number 1.1660.2017/PCh]; the Russian Foundation for Basic Research [grant number 15-01-04864], [grant number 16-01-00015], [grant number 17-51-53180].