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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.01026","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-01T20:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"530ba405768293923ae77e880ec56b70da13494fd499e434a14d1abed0637568","abstract_canon_sha256":"61d5acf60f51d1bf55094afe23d79c2bd47575e1196f5652d75c8b3ca0950ff1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:54.360172Z","signature_b64":"Q8zXVXkqPYIQNE7gG1v2v/43EbFsacI8W2MyopBZ6BE1HHLqnNNYmCMuQeSh5OtRehSJOw93J8UpIzZsG5KsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a5dcc0ecde1cdd10037ca9fbfd0b52ac76519c99020ede6dea9076d285322df","last_reissued_at":"2026-07-05T09:29:54.359651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:54.359651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 \\). 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