{"paper":{"title":"On the Schr\\\"odinger-Maxwell system involving sublinear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru Krist\\'aly, Du\\v{s}an Repov\\v{s}","submitted_at":"2016-02-12T18:20:02Z","abstract_excerpt":"In this paper we study the coupled Schr\\\"odinger-Maxwell system $$\\left\\{ \\begin{array}{lll} -\\triangle u+u +\\phi u=\\lambda \\alpha(x) f(u)& {\\rm in} & \\mathbb R^3,\\\\ -\\triangle \\phi =u^2 & {\\rm in} & \\mathbb R^3, \\end{array}\\right. $$ where $\\alpha\\in L^\\infty(\\mathbb R^3)\\cap L^{6/(5-q)}(\\mathbb R^3)$ for some $q\\in (0,1)$, and the continuous function $f:\\mathbb{R}\\to\\mathbb{R}$ is superlinear at zero and sublinear at infinity, e.g., $f(s) = \\min(|s|^r,|s|^p)$ with $0<r<1<p.$ Depending on the range of $\\lambda>0$, non-existence and multiplicity results are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04147","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"}