{"paper":{"title":"Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liejun Shen, Xiaohua Yao","submitted_at":"2017-02-13T14:44:31Z","abstract_excerpt":"The present study is concerned with the following Schr\\\"{o}dinger-Poisson system involving critical nonlocal term $$ \\left\\{ \\begin{array}{ll} -\\Delta u+u-K(x)\\phi |u|^3u=\\lambda f(x)|u|^{q-2}u, & x\\in\\mathbb{R}^3, -\\Delta \\phi=K(x)|u|^5, & x\\in\\mathbb{R}^3,\\\\ \\end{array} \\right. $$ where $1<q<2$ and $\\lambda>0$ is a parameter. Under suitable assumptions on $K(x)$ and $f(x)$, there exists $\\lambda_0=\\lambda_0(q,S,f,K)>0$ such that for any $\\lambda\\in(0,\\lambda_0)$, the above Schr\\\"{o}dinger-Poisson system possesses at least two positive solutions by standard variational method, where a positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03792","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"}