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Under the assumptions that $\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$ wit"},"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":"2405.05832","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-05-09T15:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"a0561a0c925fc0051a79fe2ec6c0e70f5ecfccda93e8f1c313a272cb02dbefa3","abstract_canon_sha256":"5481913c88bd23d469a03721b0ea807a139e64c7855ef578aae5192b7e566bf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:33.554088Z","signature_b64":"a98WVzH7jnikI6Cdp/U0taiBoprJnj1x0X9sZDQnWQkP6rv/rFiNm4t/h5gi9t9Z7uxgL5wvDQSW0RcS9gVECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05290c8c1f37fbeac4d05f29f8809971382ad63e151f5429684a2db91388f695","last_reissued_at":"2026-07-05T08:17:33.553577Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:33.553577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaushik Bal, Stuti Das","submitted_at":"2024-05-09T15:12:44Z","abstract_excerpt":"We will prove multiplicity results for the mixed local-nonlocal elliptic equation of the form \\begin{eqnarray} \\begin{split} -\\Delta_pu+(-\\Delta)_p^s u&=\\frac{\\lambda}{u^{\\gamma}}+u^r \\text { in } \\Omega, \\\\u&>0 \\text{ in } \\Omega,\\\\u&=0 \\text { in }\\mathbb{R}^n \\backslash \\Omega; \\end{split} \\end{eqnarray} where \\begin{equation*} (-\\Delta )_p^s u(x)= c_{n,s}\\operatorname{P.V.}\\int_{\\mathbb{R}^n}\\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}} d y, \\end{equation*} and $-\\Delta_p$ is the usual $p$-Laplace operator. 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