{"paper":{"title":"On The Fu\\v{c}ik Spectrum Of Non-Local Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"K.Sreenadh, Sarika Goyal","submitted_at":"2013-06-20T06:03:07Z","abstract_excerpt":"In this article, we study the Fu\\v{c}ik spectrum of fractional Laplace operator which is defined as the set of all $(\\al,\\ba)\\in \\mb\n  R^2$ such that\n  \\begin{equation*}\n  \\quad \\left. \\begin{array}{lr}\n  \\quad (-\\De)^s u = \\al u^{+} - \\ba u^{-} \\; \\text{in}\\; \\Om\n  \\quad \\quad \\quad \\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om.\\\\ \\end{array} \\quad \\right\\} \\end{equation*} has a non-trivial solution $u$, where $\\Om$ is a bounded domain in $\\mb R^n$ with Lipschitz boundary, $n>2s$, $s\\in(0,1)$. The existence of a first nontrivial curve $\\mc C$ of this spectrum, some properties of this curve "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4761","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"}