{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GWC6KCELVZKJ3LOXQLRJLL7YRJ","short_pith_number":"pith:GWC6KCEL","schema_version":"1.0","canonical_sha256":"3585e5088bae549dadd782e295aff88a476b606cd931e2bfe9f0eb8fee88e48d","source":{"kind":"arxiv","id":"1501.06302","version":1},"attestation_state":"computed","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 $(N-1)p-N<\\alpha 0$, $2 \\leq p < \\frac{2N}{N-1}$, $V \\colon \\mathbb{R}^N \\to \\mathbb{R}$ 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