{"paper":{"title":"Existence and concentration of positive solutions for nonlinear Kirchhoff type problems with a general critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David G. Costa, Jianjun Zhang, Jo\\~ao Marcos do \\'O","submitted_at":"2017-03-15T12:24:42Z","abstract_excerpt":"We are concerned with the following Kirchhoff type equation $$-\\varepsilon^2 M \\left(\\varepsilon^{2-N} \\int_{\\mathbb{R}^N} | \\nabla u|^2\\, \\mathrm{d} x\\right) \\Delta u+V(x)u = f(u),\\ x \\in \\mathbb{R}^N,\\ \\ N\\ge2, $$ where $M \\in C(\\mathbb{R}^+,\\mathbb{R}^+)$, $V\\in C(\\mathbb{R}^N,\\mathbb{R}^+)$ and $f(s)$ is of critical growth. In this paper, we construct a localized bound state solution concentrating at a local minimum of $V$ as $\\varepsilon\\to 0$ under certain conditions on $f(s)$, $M$ and $V$. In particular, the monotonicity of $f(s)/s$ and the Ambrosetti-Rabinowitz condition are not requir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05118","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"}