{"paper":{"title":"Existence of multiple solutions of $p$-fractional Laplace operator with sign-changing weight function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K.Sreenadh, Sarika Goyal","submitted_at":"2014-08-20T09:13:50Z","abstract_excerpt":"In this article, we study the following $p$-fractional Laplacian equation\n  \\begin{equation*}\n  (P_{\\la}) \\left\\{ \\begin{array}{lr} - 2\\int_{\\mb R^n}\\frac{|u(y)-u(x)|^{p-2}(u(y)-u(x))}{|x-y|^{n+p\\al}} dy = \\la |u(x)|^{p-2}u(x) + b(x)|u(x)|^{\\ba-2}u(x)\\; \\text{in}\\; \\Om\n  \\quad \\quad\\quad\\quad \\quad\\quad\\quad\\quad\\quad \\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om,\\quad u\\in W^{\\al,p}(\\mb R^n).\\\\ \\end{array} \\quad \\right. \\end{equation*} where $\\Om$ is a bounded domain in $\\mb R^n$ with smooth boundary, $n> p\\al$, $p\\geq 2$, $\\al\\in(0,1)$, $\\la>0$ and $b:\\Om\\subset\\mb R^n \\ra \\mb R$ is a sign"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4571","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":""},"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"}