{"paper":{"title":"Singularly perturbed fractional Schr\\\"{o}dinger equation involving a general critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua Jin, Jianjun Zhang, Wenbin Liu","submitted_at":"2016-11-23T03:53:45Z","abstract_excerpt":"In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schr\\\"{o}dinger problem \\begin{align*} \\varepsilon^{2s}(-\\Delta)^su+V(x)u=f(u) \\ \\ \\ \\mbox{in} \\ \\ \\ \\mathbb{R}^N, \\end{align*} where $N>2s$ and the nonlinearity $f$ has critical growth. By using the variational approach, we construct a localized bound-state solution concentrating around an isolated component of the positive minimum point of $V$ as $\\varepsilon\\rightarrow 0$. Our result improves the study made in X. He and W. Zou ({\\it Calc. Var. Partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07632","kind":"arxiv","version":2},"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"}