{"paper":{"title":"Multiple solutions for a nonhomogeneous Schr\\\"odinger-Maxwell system in $R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Yongsheng Jiang, Zhengping Wang","submitted_at":"2012-04-16T04:30:02Z","abstract_excerpt":"The paper considers the following nonhomogeneous Schr\\\"odinger-Maxwell system -\\Delta u + u+\\lambda\\phi (x) u =|u|^{p-1}u+g(x),\\ x\\in \\mathbb{R}^3, -\\Delta\\phi = u^2, \\ x\\in \\mathbb{R}^3, . \\leqno{(SM)} where $\\lambda>0$, $p\\in(1,5)$ and $g(x)=g(|x|)\\in L^2(\\mathbb{R}^3)\\setminus{0}$.\n  There seems no any results on the existence of multiple solutions to problem (SM) for $p \\in (1,3]$. In this paper, we find that there is a constant$C_p>0$ such that problem (SM) has at least two solutions for all $p\\in (1,5)$ provided\n  $\\|g\\|_{L^2} \\leq C_p$, but only for $p\\in(1,2]$ we need $\\lambda>0$ is sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3359","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"}