{"paper":{"title":"On a class of mixed Choquard-Schr\\\"odinger-Poisson system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gurpreet Singh, Marius Ghergu","submitted_at":"2016-09-13T12:23:09Z","abstract_excerpt":"We study the system $$ \\left\\{ -\\Delta u+u+K(x) \\phi |u|^{q-2}u&=(I_\\alpha*|u|^p)|u|^{p-2}u &&\\mbox{ in }{\\mathbb R}^N, -\\Delta \\phi&=K(x)|u|^q&&\\mbox{ in }{\\mathbb R}^N, \\right. $$ where $N\\geq 3$, $\\alpha\\in (0,N)$, $p,q>1$ and $K\\geq 0$. Using a Pohozaev type identity we first derive conditions in terms of $p,q,N,\\alpha$ and $K$ for which no solutions exist. Next, we discuss the existence of a ground state solution by using a variational approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03793","kind":"arxiv","version":2},"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"}