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arXiv · 2304.00786

A Liouville theorem for elliptic equations with a potential on infinite graphs

Stefano Biagi·Giulia Meglioli·Fabio Punzo
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Abstract

We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is $u\equiv 0$. We also show that on a special class of graphs the condition on the potential is optimal, in the sense that if it fails, then there exist infinitely many bounded solutions.

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Stefano Biagi, Giulia Meglioli, Fabio Punzo. 2023-04-03. A Liouville theorem for elliptic equations with a potential on infinite graphs. https://arxiv.org/abs/2304.00786

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