On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm–Liouville problem with a singular potential

  • Alexander Gomilko

    Nicolaus Copernicus University, Toruń, Poland
  • Łukasz Rzepnicki

    Nicolaus Copernicus University, Toruń, Poland
On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm–Liouville problem with a singular potential cover

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Abstract

The main focus of this paper is the following matrix Cauchy problem for the Dirac system on the interval [0,1]:

where is a spectral parameter, and , . We propose a new approach for the study of asymptotic behaviour of its solutions as and . As an application, we obtain new, sharp asymptotic formulas for eigenfunctions of Sturm–Liouville operators with singular potentials.

Cite this article

Alexander Gomilko, Łukasz Rzepnicki, On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm–Liouville problem with a singular potential. J. Spectr. Theory 10 (2020), no. 3, pp. 747–786

DOI 10.4171/JST/311