{"paper":{"title":"Constrained energy minimization and orbital stability for the NLS equation on a star graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"C. Cacciapuoti, D. Finco, D. Noja, R. Adami","submitted_at":"2012-11-07T11:21:43Z","abstract_excerpt":"We consider a nonlinear Schr\\\"odinger equation with focusing nonlinearity of power type on a star graph ${\\mathcal G}$, written as $ i \\partial_t \\Psi (t) = H \\Psi (t) - |\\Psi (t)|^{2\\mu}\\Psi (t)$, where $H$ is the selfadjoint operator which defines the linear dynamics on the graph with an attractive $\\delta$ interaction, with strength $\\alpha < 0$, at the vertex. The mass and energy functionals are conserved by the flow. We show that for $0<\\mu<2$ the energy at fixed mass is bounded from below and that for every mass $m$ below a critical mass $m^*$ it attains its minimum value at a certain $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1515","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":""},"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"}