{"paper":{"title":"Least energy radial sign-changing solution for the Schr\\\"oinger-Poisson system in r3 under an asymptotically cubic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edwin G. Murcia, Gaetano Siciliano","submitted_at":"2018-05-01T10:01:23Z","abstract_excerpt":"In this paper we consider the following Schr\\\"odinger-Poisson system in the whole $\\mathbb R^{3}$, \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  -\\Delta u+u+ \\lambda \\phi u=f(u) &\\text{ in } \\mathbb R^3,\n  -\\Delta \\phi= u^2 &\\text{ in } \\mathbb R^3,\n  \\end{array}\n  \\right. \\end{equation*} where $\\lambda>0$ and the nonlinearity $f$ is \"asymptotically cubic\" at infinity. This implies that the nonlocal term $\\phi u$ and the nonlinear term $f(u)$ are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00259","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"}