{"paper":{"title":"Comparison principle for Singular Fractional $ g- $Laplacian Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelhamid Gouasmia, Kaushik Bal","submitted_at":"2025-07-27T08:10:13Z","abstract_excerpt":"In this paper, we establish a novel comparison principle of independent interest and prove the uniqueness of weak solutions within the local Orlicz--Sobolev space framework, for the following class of fractional elliptic problems:\n  \\begin{equation*}\n  (-\\Delta)^{s}_{g} u = f(x) u^{-\\alpha} + k(x) u^{\\beta}, \\quad u > 0 \\quad \\text{in } \\Omega; \\quad u = 0 \\quad \\text{in } \\mathbb{R}^{N} \\setminus \\Omega,\n  \\end{equation*}\n  where \\( \\Omega \\subset \\mathbb{R}^{N} \\) is a smooth bounded domain, \\( \\alpha > 0 \\), and \\( \\beta > 0 \\) satisfies a suitable upper bound. Here, \\( (-\\Delta)^{s}_{g} \\)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21185","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/2507.21185/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"}