PreprintarXiv licencearXiv
Nonexistence of Stable Solutions to the Liouville Equation on Graphs with Polynomial Volume Growth
Abstract
We study stable solutions of the discrete Liouville equation −Δu=eu on infinite, locally finite graphs with polynomial volume growth. We prove that no stable solution exists whenever the order d of polynomial volume growth satisfies d<10.
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BibTeX
@misc{guan2026nonexistence,
title = {{Nonexistence of Stable Solutions to the Liouville Equation on Graphs with Polynomial Volume Growth}},
author = {Weiqi Guan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41137},
eprint = {2610.41137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41137},
}
RIS
TY - UNPB
TI - Nonexistence of Stable Solutions to the Liouville Equation on Graphs with Polynomial Volume Growth
AU - Weiqi Guan
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41137
UR - https://arxiv.org/abs/2610.41137
AB - We study stable solutions of the discrete Liouville equation −Δu=e^u on infinite, locally finite graphs with polynomial volume growth. We prove that no stable solution exists whenever the order d of polynomial volume growth satisfies d<10.
ER -