{"paper":{"title":"A new class of multiple nonlocal problems with two parameters and variable-order fractional $p(\\cdot)$-Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lamine Mbarki, Mohamed Karim Hamdani, Mostafa Allaoui","submitted_at":"2023-09-09T21:50:58Z","abstract_excerpt":"In the present manuscript, we focus on a novel tri-nonlocal Kirchhoff problem, which involves the $p(x)$-fractional Laplacian equations of variable order. The problem is stated as follows: \\begin{eqnarray*} \\left\\{\n  \\begin{array}{ll}\n  M\\Big(\\sigma_{p(x,y)}(u)\\Big)(-\\Delta)^{s(\\cdot)}_{p(\\cdot)}u(x) =\\lambda |u|^{q(x)-2}u\\left(\\int_\\O\\frac{1}{q(x)} |u|^{q(x)}dx \\right)^{k_1}+\\beta|u|^{r(x)-2}u\\left(\\int_\\O\\frac{1}{r(x)} |u|^{r(x)}dx \\right)^{k_2}\n  \\quad \\mbox{in }\\Omega,\n  \\\\ u=0 \\quad \\mbox{on }\\partial\\Omega, \\end{array} \\right. \\end{eqnarray*} where the nonlocal term is defined as $$ \\sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04879","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/2309.04879/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"}