{"paper":{"title":"Ground states of the planar nonlinear Schr\\\"odinger--Newton system with a point interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gustavo de Paula Ramos","submitted_at":"2025-06-22T23:36:43Z","abstract_excerpt":"We establish sufficient conditions for the existence of ground states of the following normalized nonlinear Schr\\\"odinger--Newton system with a point interaction: \\[ \\begin{cases} - \\Delta_\\alpha u = w u + \\beta u |u|^{p - 2} &\\text{on} ~ \\mathbb{R}^2; \\\\ - \\Delta w = 2 \\pi |u|^2 &\\text{on} ~ \\mathbb{R}^2; \\\\ \\|u\\|_{L^2}^2 = c, \\end{cases} \\] where $p > 2$; $\\alpha, \\beta \\in \\mathbb{R}$ and $- \\Delta_\\alpha$ denotes the Laplacian of point interaction with scattering length $(- 2 \\pi \\alpha)^{- 1}$. Additionally, we show that critical points of the corresponding constrained energy functional a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18202","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/2506.18202/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"}