{"paper":{"title":"Existence and multiplicity results for a new $p(x)$-Kirchhoff problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Harrabi, D.D. Repov\\v{s}, F. Mtiri, M.K. Hamdani","submitted_at":"2019-08-22T13:38:45Z","abstract_excerpt":"We study the existence and multiplicity results for the following nonlocal $p(x)$-Kirchhoff problem: \\begin{equation}\n  \\label{10} \\begin{cases} -\\left(a-b\\int_\\Omega\\frac{1}{p(x)}| \\nabla u| ^{p(x)}dx\\right)div(|\\nabla u| ^{p(x)-2}\\nabla u)=\\lambda |u| ^{p(x)-2}u+g(x,u) \\mbox{ in } \\Omega, \\\\ u=0,\\mbox{ on } \\partial\\Omega, \\end{cases} \\end{equation} where $a\\geq b > 0$ are constants, $\\Omega\\subset \\mathbb{R}^N$ is a bounded smooth domain, $p\\in C(\\overline{\\Omega})$ with $N>p(x)>1$, $\\lambda$ is a real parameter and $g$ is a continuous function. The analysis developed in this paper proposes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08369","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/1908.08369/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"}