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

Varun Bhardwaj; Rudi Weikard

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arXiv · 2309.05068

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

Varun Bhardwaj·Rudi Weikard

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Abstract

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.

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BibTeX RIS

Varun Bhardwaj, Rudi Weikard. 2023-09-10. The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients. https://arxiv.org/abs/2309.05068

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