{"paper":{"title":"Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems","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, Miguel Ramos","submitted_at":"2014-09-19T15:22:35Z","abstract_excerpt":"In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with H\\'enon-type weights \\[ -\\Delta u = |x|^{\\beta} |v|^{q-1}v, \\quad -\\Delta v =|x|^{\\alpha}|u|^{p-1}u\\quad { in } \\Omega, \\qquad u=v=0 { on } \\partial \\Omega, \\] where $\\Omega$ is a bounded smooth domain in $\\mathbb{R}^N$, $N\\geq 1$, $\\alpha, \\beta \\geq 0$ and the nonlinearities are superlinear and subcritical, namely \\[ 1> \\frac{1}{p+1}+\\frac{1}{q+1}> \\frac{N-2}{N}. \\] When $\\Omega$ is either a ball or an annulus centred at the origin and $N \\geq 2$, we show that these solutions display the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5693","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"}