{"paper":{"title":"Global bifurcation for fractional $p$-Laplacian and application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Leandro M. Del Pezzo","submitted_at":"2014-12-15T19:02:15Z","abstract_excerpt":"We prove the existence of an unbounded branch of solutions to the non-linear non-local equation $$ (-\\Delta)^s_p u=\\lambda |u|^{p-2}u + f(x,u,\\lambda) \\quad\\text{in}\\quad \\Omega,\\quad u=0 \\quad\\text{in}\\quad \\mathbb{R}^n\\setminus\\Omega, $$ bifurcating from the first eigenvalue. Here $(-\\Delta)^s_p$ denotes the fractional $p$-Laplacian and $\\Omega\\subset\\mathbb{R}^n$ is a bounded regular domain. The proof of the bifurcation results relies in computing the Leray--Schauder degree by making an homotopy respect to $s$ (the order of the fractional $p$-Laplacian) and then to use results of local case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4722","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":""},"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"}