{"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. Under the assumptions that $\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05832","kind":"arxiv","version":2},"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/2405.05832/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"}