{"paper":{"title":"On the first curve of Fu\\v{c}ik Spectrum Of $p$-fractional Laplacian Operator with nonlocal normal boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Divya Goel, K. Sreenadh, Sarika Goyal","submitted_at":"2017-10-18T01:47:34Z","abstract_excerpt":"In this article, we study the Fu\\v{c}ik spectrum of the $p$-fractional Laplace operator with nonlocal normal derivative conditions which is defined as the set of all $(a,b)\\in \\mb R^2$ such that $$ \\mc (F_p)\\left\\{ \\begin{array}{lr} \\Lambda_{n,p}(1-\\al)(-\\Delta)_{p}^{\\al} u + |u|^{p-2}u = \\frac{\\chi_{\\Omega_\\e}}{\\e} (a (u^{+})^{p-1} - b (u^{-})^{p-1}) \\;\\quad \\text{in}\\; \\Omega,\\quad \\\\ \\mc{N}_{\\al,p} u = 0 \\; \\quad \\mbox{in}\\; \\mb R^n \\setminus \\overline{\\Omega}, \\end{array} \\right. $$ has a non-trivial solution $u$, where $\\Omega$ is a bounded domain in $\\mb R^n$ with Lipschitz boundary, $p "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07217","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"}