{"paper":{"title":"Bound state nodal solutions for the non-autonomous Schr\\\"{o}dinger--Poisson system 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":"2018-12-07T14:39:47Z","abstract_excerpt":"In this paper, we study the existence of nodal solutions for the non-autonomous Schr\\\"{o}dinger--Poisson system: \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\Delta u+u+\\lambda K(x) \\phi u=f(x) |u|^{p-2}u & \\text{ in }\\mathbb{R}^{3}, \\\\ -\\Delta \\phi =K(x)u^{2} & \\text{ in }\\mathbb{R}^{3},% \\end{array}% \\right. \\end{equation*}% where $\\lambda >0$ is a parameter and $2<p<4$. Under some proper assumptions on the nonnegative functions $K(x)$ and $f(x)$, but not requiring any symmetry property, when $\\lambda$ is sufficiently small, we find a bounded nodal solution for the above problem by proposing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03042","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"}