{"paper":{"title":"Normalized Solutions on large smooth domains to the Schr\\\"{o}dinger equation with potential and general nonlinearity: Mass super-critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaolu Lin, Zongyan Lv","submitted_at":"2025-01-06T05:11:29Z","abstract_excerpt":"In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schr\\\"{o}dinger equation with general nonlinearity: Mass super-critical case: \\[\\begin{cases} -\\Delta u+V(x)u+\\lambda u=g(u),\\\\ \\|u\\|_2^2=\\int|u|^2\\mathrm{d}x=c, \\end{cases} \\] both on large bounded smooth star-shaped domain $\\Omega\\subset\\mathbb{R}^N$ and on $\\mathbb{R}^N$, where $V(x)$ is the potential and the nonlinearity $g(\\cdot)$ considered here are very general and of mass super-critical. The standard approach based on the Pohozaev identity to obtain normalized solutions is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04893","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/2501.04893/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"}