{"paper":{"title":"Problem involving nonlocal operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amita Soni, D. Choudhuri, Ratan Kr. Giri","submitted_at":"2017-07-12T10:40:06Z","abstract_excerpt":"The aim of this paper is to deal with the elliptic pdes involving a nonlinear integrodifferential operator, which are possibly degenerate and covers the case of fractional $p$-Laplacian operator. We prove the existence of a solution in the weak sense to the problem \\begin{align*} \\begin{split} -\\mathscr{L}_\\Phi u & = \\lambda |u|^{q-2}u\\,\\,\\mbox{in}\\,\\,\\Omega,\\\\ u & = 0\\,\\, \\mbox{in}\\,\\, \\mathbb{R}^N\\setminus \\Omega \\end{split} \\end{align*} if and only if a weak solution to \\begin{align*} \\begin{split} -\\mathscr{L}_\\Phi u & = \\lambda |u|^{q-2}u +f,\\,\\,\\,f\\in L^{p'}(\\Omega),\\\\ u & = 0\\,\\, \\mbox{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03636","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"}