{"paper":{"title":"A degenerate Kirchhoff-type problem involving variable $s(\\cdot)$-order fractional $p(\\cdot)$-Laplacian with weights","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lamine Mbarki, Mohamed Karim Hamdani, Mostafa Allaoui","submitted_at":"2023-08-15T19:45:23Z","abstract_excerpt":"This paper deals with a class of nonlocal variable $s(.)$-order fractional $p(.)$-Kirchhoff type equations: \\begin{eqnarray*} \\left\\{\n  \\begin{array}{ll}\n  \\mathcal{K}\\left(\\int_{\\mathbb{R}^{2N}}\\frac{1}{p(x,y)}\\frac{|\\varphi(x)-\\varphi(y)|^{p(x,y)}}{|x-y|^{N+s(x,y){p(x,y)}}} \\,dx\\,dy\\right)(-\\Delta)^{s(\\cdot)}_{p(\\cdot)}\\varphi(x) =f(x,\\varphi)\n  \\quad \\mbox{in }\\Omega,\n  \\\\ \\varphi=0 \\quad \\mbox{on }\\mathbb{R}^N\\backslash\\Omega. \\end{array} \\right. \\end{eqnarray*} Under some suitable conditions on the functions $p,s, \\mathcal{K}$ and $f$, the existence and multiplicity of nontrivial solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.08007","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/2308.08007/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"}