{"paper":{"title":"Existence of solutions to a generalized self-dual Chern-Simons equation on finite graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuanyang Hu","submitted_at":"2022-02-05T10:08:07Z","abstract_excerpt":"Let $G=(V,E)$ be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on $G$ \\begin{equation*}\n  \\Delta u=\\lambda \\mathrm{e}^{u}\\left(\\mathrm{e}^{u}-1\\right)^{5}+4 \\pi \\sum_{s=1}^{N} \\delta_{p_{s}} \\quad , \\end{equation*} where $\\lambda>0$, $\\delta_{p_{s}}$ is the Dirac mass at the vetex $p_s$, and $p_1, p_2,\\dots, p_N$ are arbitrarily chosen distinct vertices on the graph. We show that there exists a critial value $\\hat{\\lambda}$ such that when $\\lambda > \\hat{\\lambda}$, the generalized Chern-Simons equation has at least two solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02525","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.02525/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}