Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Fedoseev A. E. Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point. Izv. Sarat. Univ. Math. Mech. Inform., 2012, vol. 12, iss. 4, pp. 49-55. DOI: 10.18500/1816-9791-2012-12-4-49-55

Published online: 
15.11.2012
Full text:
(downloads: 53)
Language: 
Russian
Heading: 
UDC: 
517.927
DOI: 
10.18500/1816-9791-2012-12-4-49-55

Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point

Autors: 
Fedoseev Alexey Evgen'evich, Saratov State University
Abstract: 

The inverse problem of recovering Sturm–Liouville operators on the half-line with a nonintegrable Bessel-type singularity in an interior point from the given Weyl function is studied. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions of the solvability of the inverse problem are obtained. 

References: 
  1. Марченко В. А. Операторы Штурма–Лиувилля и их приложения. Киев : Наук. думка, 1977. 330 с.
  2. Левитан Б. М. Обратные задачи Штурма–Лиувил- ля. М. : Наука, 1984. 239 с.
  3. Юрко В. А. Введение в теорию обратных спектраль- ных задач. М. : Физматлит, 1984. 384 с.
  4. Yurko V. A. Method of Spectral Mappings in the Inverse Problem Theory // Inverse and Ill-posed Problems Series. Utrecht : VSP, 2002. 303 p.
  5. Юрко В. А. О восстановлении сингулярных несамо- сопряженных дифференциальных операторов с особен- ностью внутри интервала // Дифференциальные урав- нения. 2002. Т. 38, № 5. С. 645–659.
  6. Fedoseev A. E. Inverse problems for differential equations on the half-line having a singularity in an interior point // Tamkang J. of Math. 2011. Vol. 42, № 3. P. 343–354.