{"paper":{"title":"On nodal solutions of a nonlocal Choquard equation in a bounded domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changfeng Gui, Hui Guo","submitted_at":"2017-10-13T18:09:37Z","abstract_excerpt":"In this paper, we are interested in the least energy nodal solutions to the following nonlocal Choquard equation with a local term \\begin{equation*}\\left\\{\\begin{array}{rll} -\\Delta u&=\\lambda|u|^{p-2}u+\\mu \\phi(x)|u|^{q-2}u\\\\ -\\Delta \\phi&=|u|^q\\\\ u&=\\phi=0 \\end{array}\\right. \\begin{gathered}\\begin{array}{rll} &\\mbox{in}\\ \\Omega,\\\\ &\\mbox{in}\\ \\Omega,\\\\ &\\mbox{on}\\ \\partial\\Omega, \\end{array}\\end{gathered}\\end{equation*} where $ \\lambda,\\mu>0, p\\in [2,6), q\\in (1,5)$ and $\\Omega\\subset \\mathbb{R}^3$ is a bounded domain. This problem may be seen as a nonlocal perturbation of the classical Lane"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05040","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"}