{"paper":{"title":"On the non-autonomous Schr\\\"odinger-Poisson problems in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu","submitted_at":"2014-08-19T11:41:14Z","abstract_excerpt":"In this paper, we study the problem: \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\Delta u+u+\\lambda K\\left( x\\right) \\phi u=a\\left( x\\right) \\left\\vert u\\right\\vert ^{p-2}u & \\text{ in }\\mathbb{R}^{3}, \\\\ -\\Delta \\phi =K\\left( x\\right) u^{2} & \\ \\text{in }\\mathbb{R}^{3}, \\end{array} \\right. \\end{equation*} where $\\lambda >0$ and $2<p<4$. We require that $K\\left( x\\right)$ and $a\\left( x\\right) $ are nonnegative functions in $\\mathbb{R}^{3}$ and satisfy some suitable assumptions, but not requiring any symmetry property on them. Assuming that $\\lim_{\\left\\vert x\\right\\vert \\rightarrow \\infty }K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4302","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"}