{"paper":{"title":"On the blow-up solutions for the nonlinear Schr\\\"{o}dinger equation with combined power-type nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Binhua Feng","submitted_at":"2018-03-30T05:28:16Z","abstract_excerpt":"This paper is devoted to the analysis of blow-up solutions for the nonlinear Schr\\\"{o}dinger equation with combined power-type nonlinearities \\[ iu_{t}+\\Delta u=\\lambda_1|u|^{p_1}u+\\lambda_2|u|^{p_2}u. \\] When $p_1=\\frac{4}{N}$ and $0<p_2<\\frac{4}{N}$, we prove the existence of blow-up solutions and find the sharp threshold mass of blow-up and global existence for this equation. This is a complement to the result of Tao et al. (Comm. Partial Differential Equations 32: 1281-1343, 2007). Moreover, we investigate the dynamical properties of blow-up solutions, including $L^2$-concentration, blow-u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11343","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"}