{"paper":{"title":"Existence and concentration of ground state solutions for a critical nonlocal Schr\\\"odinger equation in $\\R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Cristina Tarsi, Daniele Cassani, Minbo Yang","submitted_at":"2016-01-08T01:33:46Z","abstract_excerpt":"We study the following singularly perturbed nonlocal Schr\\\"{o}dinger equation $$ -\\vr^2\\Delta u +V(x)u =\\vr^{\\mu-2}\\Big[\\frac{1}{|x|^{\\mu}}\\ast F(u)\\Big]f(u) \\quad \\mbox{in} \\quad \\R^2, $$ where $V(x)$ is a continuous real function on $\\R^2$, $F(s)$ is the primitive of $f(s)$, $0<\\mu<2$ and $\\vr$ is a positive parameter. Assuming that the nonlinearity $f(s)$ has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01743","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"}