{"paper":{"title":"Existence results of positive solutions for Kirchhoff type equations via bifurcation methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Su\\'arez, Gaetano Siciliano, Jo\\~ao R. Santos J\\'unior, Willian Cintra","submitted_at":"2017-10-05T17:16:21Z","abstract_excerpt":"In this paper we address the following Kirchhoff type problem \\begin{equation*}\n  \\left\\{ \\begin{array}{ll}\n  -\\Delta(g(|\\nabla u|_2^2) u + u^r) = a u + b u^p& \\mbox{in}~\\Omega, u>0& \\mbox{in}~\\Omega, u= 0& \\mbox{on}~\\partial\\Omega,\n  \\end{array} \\right. \\end{equation*} in a bounded and smooth domain $\\Omega$ in ${\\rm I}\\hskip -0.85mm{\\rm R}$. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters $a,b,p,r$ and the nonlinearity $g$, the existence of positive solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02120","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"}