{"paper":{"title":"On a class of quasilinear elliptic equation with indefinite weights on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guoqing Zhang, Shoudong Man","submitted_at":"2019-03-13T07:53:03Z","abstract_excerpt":"Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $\\Omega\\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \\left \\{ \\begin{array}{lcr} -\\Delta_{p}u= \\lambda K(x)|u|^{p-2}u+f(x,u), \\ \\ x\\in\\Omega^{\\circ},\n  u=0, \\ \\ x\\in\\partial \\Omega, \\\\ \\end{array} \\right. $$ where $\\Omega^{\\circ}$ and $\\partial \\Omega$ denote the interior and the boundary of $\\Omega$ respectively, $\\Delta_{p}$ is the discrete $p$-Laplacian, $K(x)$ is a given function which may change sign, $\\lambda$ is the eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05346","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}