{"paper":{"title":"Ground states and high energy solutions of the planar Schr\\\"odinger-Poisson system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miao Du, Tobias Weth","submitted_at":"2017-03-15T11:36:03Z","abstract_excerpt":"In this paper, we are concerned with the Schr\\\"{o}dinger-Poisson system \\begin{equation} (0.1)\\qquad -\\Delta u + u +\\phi u = |u|^{p-2}u \\quad \\text{in}\\ \\mathbb{R}^{d},\\qquad \\Delta \\phi= u^{2} \\quad \\text{in}\\ \\mathbb{R}^{d}. \\end{equation} Due to its relevance in physics, the system has been extensively studied and is quite well understood in the case $d \\ge 3$. In contrast, much less information is available in the planar case $d=2$ which is the focus of the present paper. It has been observed by Cingolani and the second author \\cite{Cingolani-Weth-2016} that the variational structure of $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05090","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"}