{"paper":{"title":"Bound state solutions for the supercritical fractional Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hardy Chan, Juncheng Wei, Maria del Mar Gonzalez, Weiwei Ao","submitted_at":"2018-05-08T09:25:21Z","abstract_excerpt":"We prove the existence of positive solutions for the supercritical nonlinear fractional Schr\\\"odinger equation $(-\\Delta)^s u+V(x)u-u^p=0$ in $\\mathbb R^n$, with $u(x)\\to 0$ as $|x|\\to +\\infty$, where $p>\\frac{n+2s}{n-2s}$ for $s\\in (0,1), \\ n>2s$. We show that if $V(x)=o(|x|^{-2s})$ as $|x|\\to +\\infty$, then for $p>\\frac{n+2s-1}{n-2s-1}$, this problem admits a continuum of solutions. More generally, for $p>\\frac{n+2s}{n-2s}$, conditions for solvability are also provided. This result is the extension of the work by Davila, Del Pino, Musso and Wei to the fractional case. Our main contributions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02915","kind":"arxiv","version":2},"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"}