{"paper":{"title":"On critical and supercritical pseudo-relativistic nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinmyoung Seok, Woocheol Choi, Younghun Hong","submitted_at":"2017-05-25T06:54:38Z","abstract_excerpt":"In this paper, we investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schr\\\"odinger equation $$\\left( \\sqrt{-c^2\\Delta + m^2 c^4}-mc^2\\right) u + \\mu u = |u|^{p-1}u\\quad \\textrm{in}~\\mathbb{R}^n~(n \\geq 2)$$ involving an $H^{1/2}$-critical/supercritical power-type nonlinearity, i.e., $p \\geq \\frac{n+1}{n-1}$. We prove that in the non-relativistic regime, there exists a nontrivial solution provided that the nonlinearity is $H^{1/2}$-critical/supercritical but it is $H^1$-subcritical. On the other hand, we also show that there is no nontrivial bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09068","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"}