{"paper":{"title":"Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential 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","submitted_at":"2009-04-29T13:49:03Z","abstract_excerpt":"We study the following Schr\\\"odinger-Poisson system (P_\\lambda){ll}\n  -\\Delta u + V(x)u+\\lambda \\phi (x) u =Q(x)u^{p}, x\\in \\mathbb{R}^3 \\\\\n  -\\Delta\\phi = u^2, \\lim\\limits_{|x|\\to +\\infty}\\phi(x)=0, u>0, where $\\lambda\\geqslant0$ is a parameter, $1 < p < +\\infty$, $V(x)$ and $Q(x)$ are sign-changing or non-positive functions in $ L^{\\infty}(\\mathbb{R}^3)$. When $V(x)\\equiv Q(x)\\equiv1$, D.Ruiz \\cite{RuizD-JFA} proved that ($P_\\lambda$) with $p\\in(2,5)$ has always a positive radial solution, but ($P_\\lambda$) with $p\\in(1,2]$ has solution only if $\\lambda>0$ small enough and no any nontrivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4611","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"}