The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients
- Resource Type
- Working Paper
- Authors
- Bhardwaj, Varun; Weikard, Rudi
- Source
- Subject
- Mathematics - Spectral Theory
Mathematical Physics
Mathematics - Classical Analysis and ODEs
34B20 (Primary) 34L05, 47B25 (Secondary)
- Language
We investigate the limit-point/limit-circle classification for the differential equation $Ju'+qu=\lambda wu$ where $J=\big(\begin{smallmatrix}0&-1\\ 1&0\end{smallmatrix}\big)$ and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$ non-negative. We identify the situations when the classical alternative of Weyl works and when it fails.