{"paper":{"title":"On the Schrodinger-Poisson-Slater system: behavior of minimizers, radial and nonradial cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Ruiz","submitted_at":"2009-04-19T17:31:41Z","abstract_excerpt":"This paper is motivated by the study of a version of the so-called Schrodinger-Poisson-Slater problem: $$ - \\Delta u + \\omega u + \\lambda (u^2 \\star \\frac{1}{|x|}) u=|u|^{p-2}u,$$ where $u \\in H^1(\\R^3)$. We are concerned mostly with $p \\in (2,3)$. The behavior of radial minimizers motivates the study of the static case $\\omega=0$. Among other things, we obtain a general lower bound for the Coulomb energy, that could be useful in other frameworks. The radial and nonradial cases turn out to yield essentially different situations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2924","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"}