{"paper":{"title":"Normalized solutions to Sch\\\"odinger equations with potential and inhomogeneous nonlinearities on large convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shijie Qi, Thomas Bartsch, Wenming Zou","submitted_at":"2023-06-13T14:57:58Z","abstract_excerpt":"The paper addresses an open problem raised in [Bartsch, Molle, Rizzi, Verzini: Normalized solutions of mass supercritical Schr\\\"odinger equations with potential, Comm. Part. Diff. Equ. 46 (2021), 1729-1756] on the existence of normalized solutions to Schr\\\"odinger equations with potentials and inhomogeneous nonlinearities. We consider the problem \\[\n  -\\Delta u+V(x)u+\\lambda u = |u|^{q-2}u+\\beta |u|^{p-2}u, \\quad \\|u\\|^2_2=\\int|u|^2dx = \\alpha, \\] both on $\\mathbb{R}^N$ as well as on domains $r\\Omega$ where $\\Omega\\subset\\mathbb{R}^N$ is an open bounded convex domain and $r>0$ is large. The ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07826","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/2306.07826/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"}