{"paper":{"title":"Stable standing waves for a class of nonlinear Schroedinger-Poisson equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Jacopo Bellazzini","submitted_at":"2010-02-09T11:54:11Z","abstract_excerpt":"We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following  Schr\\\"odinger-Poisson type equation \\label{intro} %{%{ll} i\\psi_{t}+ \\Delta \\psi - (|x|^{-1}*|\\psi|^{2}) \\psi+|\\psi|^{p-2}\\psi=0  \\text{in} \\R^{3}, %-\\Delta\\phi= |\\psi|^{2}& \\text{in} \\R^{3},%. when $p\\in \\{8/3\\}\\cup (3,10/3)$.  In the case $3<p<10/3$ we prove the existence  and stability only for sufficiently large $L^2$-norm. In case $p=8/3$  our approach recovers  the result of Sanchez and Soler \\cite{SS} %concerning the existence and stability for sufficiently small charges. The main poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1830","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"}