{"paper":{"title":"Some existence and nonexistence results for a Schr\\\"odinger-Poisson type system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yutian Lei","submitted_at":"2014-11-06T08:22:09Z","abstract_excerpt":"In this paper, we study the Schr\\\"odinger-Poisson system $$ \\left \\{ \\begin{array}{l} -\\Delta u=\\sqrt{p}u^{p-1}v, \\quad u>0 \\quad in \\quad R^n, -\\Delta v=\\sqrt{p}u^p, \\quad v>0 \\quad in \\quad R^n \\end{array} \\right. $$ with $n \\geq 3$ and $p>1$. We investigate the existence and the nonexistence of positive classical solutions with the help of an integral system involving the Newton potential $$ \\left \\{ \\begin{array}{l} u(x)=c_1\\displaystyle\\int_{R^n}\\frac{u^{p-1}(y)v(y)dy}{|x-y|^{n-2}}, \\quad u>0 \\quad in \\quad R^n, v(x)=c_2\\displaystyle\\int_{R^n}\\frac{u^p(y)dy}{|x-y|^{n-2}} \\quad v>0 \\quad i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1523","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"}