{"paper":{"title":"The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liejun Shen, Xiaohua Yao","submitted_at":"2017-02-13T14:25:08Z","abstract_excerpt":"The present study is concerned with the following Schr\\\"{o}dinger-Poisson system involving critical nonlocal term with general nonlinearity: $$ \\left\\{ \\begin{array}{ll} -\\Delta u+V(x)u- \\phi |u|^3u= f(u), & x\\in\\mathbb{R}^3, -\\Delta \\phi= |u|^5, & x\\in\\mathbb{R}^3,\\\\ \\end{array} \\right. $$ Under certain assumptions on non-constant $V(x)$, the existence of a positive least energy solution is obtained by using some new analytical skills and Poho\\v{z}aev type manifold. In particular, the Ambrosetti-Rabinowitz type condition or monotonicity assumption on the nonlinearity is not necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03785","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"}