{"paper":{"title":"Liouville-type theorems for polyharmonic H\\'enon-Lane-Emden system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Quoc Hung Phan","submitted_at":"2014-05-19T03:07:38Z","abstract_excerpt":"We study Liouville-type theorem for polyharmonic H\\'enon-Lane-Emden system $(-\\Delta)^mu=|x|^av^p,\\; (-\\Delta)^mv=|x|^bu^q$ when $m,p,q\\geq 1, pq\\ne 1$, and $a,b\\geq 0$. It is a natural conjecture that the nonexistence of positive solutions should be true if and only if $(N+a)/(p+1)+$ $(N+b)/(q+1)>N-2m$. It is shown by Fazly [6] that the conjecture holds for radial solutions in all dimensions and for classical solutions in dimension $N\\leq 2m+1$. We here give some partial results in dimension $N\\geq 2m+2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4584","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"}