{"paper":{"title":"Ground states of a system of nonlinear Schr\\\"odinger equations with periodic potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski","submitted_at":"2014-11-20T15:56:52Z","abstract_excerpt":"We are concerned with a system of coupled Schr\\\"odinger equations $$-\\Delta u_i + V_i(x)u_i = \\partial_{u_i}F(x,u)\\hbox{ on }\\mathbb{R}^N,\\,i=1,2,...,K,$$ where $F$ and $V_i$ are periodic in $x$ and $0\\notin \\sigma(-\\Delta+V_i)$ for $i=1,2,...,K$, where $\\sigma(-\\Delta+V_i)$ stands for the spectrum of the Schr\\\"odinger operator $-\\Delta+V_i$. We impose general assumptions on the nonlinearity $F$ with the subcritical growth and we find a ground state solution being a minimizer of the energy functional associated with the system on a Nehari-Pankov manifold. Our approach is based on a new linking"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5582","kind":"arxiv","version":4},"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"}