{"paper":{"title":"Normalized Solutions to Schr\\\"{o}dinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Ji","submitted_at":"2024-09-16T14:04:07Z","abstract_excerpt":"We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\\\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass supercritical, critical, subcritical or some mixes of these cases, and the equation can be autonomous or non-autonomous. This generalizes a result in Noris, Tavares and Verzini [\\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where the equation is autonomous with homogeneous nonlinearities. Besides, we have proven some orbital stability or instability results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10299","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/2409.10299/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"}