English

The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients

Spectral Theory 2023-09-12 v1 Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

We investigate the limit-point/limit-circle classification for the differential equation Ju+qu=λwuJu'+qu=\lambda wu where J=(0110)J=\big(\begin{smallmatrix}0&-1\\ 1&0\end{smallmatrix}\big) and qq and ww are matrices whose entries are distributions of order zero with qq Hermitian and ww non-negative. We identify the situations when the classical alternative of Weyl works and when it fails.

Cite

@article{arxiv.2309.05068,
  title  = {The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients},
  author = {Varun Bhardwaj and Rudi Weikard},
  journal= {arXiv preprint arXiv:2309.05068},
  year   = {2023}
}
R2 v1 2026-06-28T12:17:25.447Z