{"paper":{"title":"A Capacitary Approach to Semilinear Elliptic Inequalities with Potentials on Weighted Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bessem Samet, Mohamed Jleli","submitted_at":"2026-06-17T23:11:28Z","abstract_excerpt":"We develop a capacitary approach to semilinear elliptic inequalities on weighted graphs with a potential. More precisely, we study the nonexistence of nontrivial nonnegative solutions of \\[ \\Delta u+w(x)u+v(x)u^\\sigma\\le0 \\qquad\\text{in }V, \\] where \\((V,\\omega,\\mu)\\) is a connected, locally finite weighted graph, \\(\\Delta\\) is the associated graph Laplacian, \\(\\sigma>1\\), \\(v>0\\), and \\(w\\) is a real-valued potential. The potential term is handled by means of a positive solution \\(H\\) of \\(\\Delta H+wH=0\\), which transforms the operator \\(\\Delta+w\\) into the \\(H\\)-Laplacian associated with a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19650","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19650/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"}