{"paper":{"title":"Semiclassical analysis for pseudo-relativistic Hartree equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Silvia Cingolani, Simone Secchi","submitted_at":"2015-01-26T09:56:36Z","abstract_excerpt":"In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\\sqrt{-\\varepsilon^2 \\Delta + m^2}u + V u = (I_\\alpha * |u|^{p})\n  |u|^{p-2}u$ in $\\mathbb{R}^N$ where $m>0$, $2 \\leq p < \\frac{2N}{N-1}$, $V \\colon \\mathbb{R}^N \\to \\mathbb{R}$ is an external scalar potential, $I_\\alpha (x) = \\frac{c_{N,\\alpha}}{|x|^{N-\\alpha}}$ is a convolution kernel, $c_{N,\\alpha}$ is a positive constant and $(N-1)p-N<\\alpha <N$. For $N=3$, $\\alpha=p=2$, our equation becomes the pseudo-relativistic Hartree equation with Coulomb kernel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06302","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"}