{"paper":{"title":"Standing Waves for nonlinear Schrodinger Equations involving critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianjun Zhang, Wenming Zou, Zhijie Chen","submitted_at":"2012-09-14T01:53:41Z","abstract_excerpt":"We consider the following singularly perturbed nonlinear elliptic problem: $$-\\e^2\\Delta u+V(x)u=f(u),\\ u\\in H^1(\\mathbb{R^N}),$$ where $N\\ge 3$ and the nonlinearity $f$ is of critical growth. In this paper, we construct a solution $u_\\e$ of the above problem which concentrates at an isolated component of positive local minimum points of $V$ as $\\e\\to 0$ under certain conditions on $f$. Our result completes the study made in some very recent works in the sense that, in those papers only the subcritical growth was considered"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3074","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"}