{"paper":{"title":"Hamiltonian elliptic systems: a guide to variational frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Bonheure, Ederson Moreira dos Santos, Hugo Tavares","submitted_at":"2014-02-14T16:15:43Z","abstract_excerpt":"Consider a Hamiltonian system of type \\[ -\\Delta u=H_{v}(u,v),\\ -\\Delta v=H_{u}(u,v) \\ \\ \\text{ in } \\Omega, \\qquad u,v=0 \\text{ on } \\partial \\Omega \\] where $H$ is a power-type nonlinearity, for instance $H(u,v)= |u|^p/p+|v|^q/q$, having subcritical growth, and $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 1$. The aim of this paper is to give an overview of the several variational frameworks that can be used to treat such a system. Within each approach, we address existence of solutions, and in particular of ground state solutions. Some of the available frameworks are more adequate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3516","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"}