{"paper":{"title":"Uniqueness Results for Mixed Local and Nonlocal Equations with Singular Nonlinearities and Source Terms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelhamid Gouasmia","submitted_at":"2024-11-01T20:52:19Z","abstract_excerpt":"This paper considers a local and non-local problem characterized by singular nonlinearity and a source term. Specifically, we focus on the following problem:\n  \\begin{equation}\\label{A}\\tag{P}\n  -\\Delta_{p} u + (-\\Delta)^{s}_{q} u = f(x) u^{-\\alpha} + g(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 an open bounded domain with a \\( C^{2} \\) boundary \\( \\partial \\Omega \\), and \\( N > p \\). We assume that \\( 0 < s < 1 \\) and \\( 1 < p, q < \\infty \\), with the conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01026","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/2411.01026/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"}