{"paper":{"title":"On a class of nonlinear Schr\\\"odinger-Poisson systems involving a nonradial charge density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlo Mercuri, Teresa Megan Tyler","submitted_at":"2018-05-02T18:21:20Z","abstract_excerpt":"In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schr\\\"odinger equations, we prove existence of mountain-pass solutions and least energy solutions to the nonlinear Schr\\\"odinger-Poisson system \\begin{equation}\\nonumber \\left\\{\\begin{array}{lll}\n  - \\Delta u+ u + \\rho (x) \\phi u = |u|^{p-1} u, \\qquad &x\\in \\mathbb R^3,\n  \\,\\,\\, -\\Delta \\phi=\\rho(x) u^2,\\ & x\\in \\mathbb R^3, \\end{array} \\right. \\end{equation} under different assumptions on $\\rho: \\mathbb R^3\\rightarrow \\mathbb R_+$ at infinity. Our results cover the range $p\\in(2,3)$ where the lack of compactness phenomena ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00964","kind":"arxiv","version":3},"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"}