{"paper":{"title":"Multiplicity results for the fractional laplacian in expanded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"G.M. Figueiredo, G. Siciliano, M. T.O Pimenta","submitted_at":"2015-11-30T17:45:06Z","abstract_excerpt":"In this paper we establish the multiplicity of nontrivial weak solutions for the problem $(-\\Delta)^{\\alpha} u +u= h(u)$ in $\\Omega_{\\lambda}$,\\ $u=0$ on $\\partial\\Omega_{\\lambda}$, where $\\Omega_{\\lambda}=\\lambda\\Omega$, $\\Omega$ is a smooth and bounded domain in $\\mathbb{R}^N, N>2\\alpha$, $\\lambda$ is a positive parameter, $\\alpha \\in (0,1)$, $(-\\Delta)^{\\alpha}$ is the fractional Laplacian and the nonlinear term $h(u)$ has a subcritical growth. We use minimax methods, the Ljusternick-Schnirelmann and Morse theories to get multiplicity result depending on the topology of $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09406","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"}