{"paper":{"title":"Positive and sign changing solutions to a nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dora Salazar, M\\'onica Clapp","submitted_at":"2012-11-25T15:51:06Z","abstract_excerpt":"We consider the problem \\[-\\Delta u + W(x)u = ((1/{|x|^{\\alpha}} * |u|^{p}) |u|^{p-2}u, u \\in H_{0}^{1}(\\Omega)\\], where $\\Omega$ is an exterior domain in $\\mathbb{R}^{N}$, $N\\geq3,$ $\\alpha \\in(0,N)$, $p\\in[2,(2N-\\alpha)/(N-2)$, $W$ is continuous, $\\inf_{\\mathbb{R}^{N}}W>0,$ and $W(x)$ tends to a positive constant as $|x|$ tends to infinity. Under symmetry assumptions on $\\Omega$ and $W$, which allow finite symmetries, and some assumptions on the decay of $W$ at infinity, we establish the existence of a positive solution and multiple sign changing solutions to this problem, having small energ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5769","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"}