{"paper":{"title":"Symmetry and classification of positive standing waves of nonlinear Hartree type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ederson Moreira dos Santos, Eduardo de Souza B\\\"oer, Gustavo de Paula Ramos","submitted_at":"2026-05-22T01:03:10Z","abstract_excerpt":"This paper presents some qualitative properties of positive solutions to the strongly coupled system \\[ \\begin{cases} \\displaystyle - \\Delta u + \\tau u =\n\\frac{2 p}{p + q} \\left( I_\\alpha \\ast |v|^q \\right) |u|^{p - 2} u &\\text{in} ~ \\mathbb{R}^N, \\\\ \\\\ \\displaystyle - \\Delta v + \\eta v =\n\\frac{2 q}{p + q} \\left( I_\\alpha \\ast |u|^p \\right) |v|^{q - 2} v &\\text{in} ~ \\mathbb{R}^N, \\end{cases} \\] with $\\tau, \\eta > 0$, $N \\in \\mathbb{N}$, $0 < \\alpha < N$, \\[ \\max \\left\\{1, \\frac{2 \\alpha}{N}\\right\\} < p, q < 2^* \\quad \\text{and} \\quad \\frac{2 (N + \\alpha)}{N} < p + q < 2_\\alpha^*, \\] where $I_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23127","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}