{"paper":{"title":"Standing waves for the Chern-Simons-Schrodinger equation with critical exponential growth","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Ji, Fei Fangb","submitted_at":"2016-07-25T03:22:19Z","abstract_excerpt":"In this paper, by combing the variational methods and Trudinger-Moser inequality, we study the existence and multiplicity of the positive standing wave for the following Chern-Simons-Schr\\\"odinger equation \\begin{equation} -\\Delta u+u +\\lambda\\left(\\int_{0}^{\\infty}\\frac{h(s)}{s}u^{2}(s)ds+\\frac{h^{2}(\\vert x\\vert)}{\\vert x\\vert^{2}}\\right)u=f(x,u)+\\epsilon k(x)\\quad\\quad \\text{in}\\,\\,\\mathbb{R}^2, \\\\ \\end{equation} where $h(s)=\\int_{0}^{s}\\frac{l}{2}u^{2}(l)dl$, $\\lambda>0$ and the nonlinearity $f:\\mathbb{R}^2\\times \\mathbb{R}\\rightarrow \\mathbb{R}$ behaves like $\\text{exp}(\\alpha\\vert u\\vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07136","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"}