{"paper":{"title":"Pohozaev identities for a pseudo-relativistic Schr\\\"odinger operator and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.H. Souza Medeiros, G.A Pereira, H. Bueno","submitted_at":"2018-10-17T15:00:47Z","abstract_excerpt":"In this paper we prove a Pohozaev-type identity for both the problem $(-\\Delta+m^2)^su=f(u)$ in $\\mathbb{R}^N$ and its harmonic extension to $\\mathbb{R}^{N+1}_+$ when $0<s<1$. So, our setting includes the pseudo-relativistic operator $\\sqrt{-\\Delta+m^2}$ and the results showed here are original, to the best of our knowledge. The identity is first obtained in the extension setting and then \"translated\" into the original problem. In order to do that, we develop a specific Fourier transform theory for the fractionary operator $(-\\Delta+m^2)^s$, which lead us to define a weak solution $u$ of the o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07597","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"}