{"paper":{"title":"Existence of solution for a nonlocal problem in $\\R^N$ via bifurcation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Marco A. S. Souto, Romildo N. de Lima","submitted_at":"2015-09-17T15:35:38Z","abstract_excerpt":"In this paper, we study the existence of solution for the following class of nonlocal problem, $$ \\left\\{ \\begin{array}{lcl} -\\Delta u=\\left(\\lambda f(x)-\\int_{\\R^N}K(x,y)|u(y)|^{\\gamma}dy\\right)u,\\quad \\mbox{in} \\quad \\R^{N}, \\\\ \\displaystyle \\lim_{|x| \\to +\\infty}u(x)=0,\\quad u>0 \\quad \\text{in} \\quad \\R^{N}, \\end{array} \\right. \\eqno{(P)} $$ where $N\\geq3$, $\\lambda >0, \\gamma\\in[1,2)$, $f:\\R\\rightarrow\\R$ is a positive continuous function and $K:\\R^N\\times\\R^N\\rightarrow\\R$ is a nonnegative function. The functions $f$ and $K$ satisfy some conditions, which permit to use Bifurcation Theory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05294","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"}