{"paper":{"title":"On the existence of bounded solutions for a nonlinear elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcela Sanmartino, Marisa Toschi, Ricardo G. Duran","submitted_at":"2010-11-01T19:05:59Z","abstract_excerpt":"This work deals with the system $(-\\Delta)^m u= a(x) v^p$, $(-\\Delta)^m v=b(x) u^q$ with Dirichlet boundary condition in a domain $\\Omega\\subset\\RR^n$, where $\\Omega$ is a ball if $n\\ge 3$ or a smooth perturbation of a ball when $n=2$.\n  We prove that, under appropriate conditions on the parameters ($a,b,p,q,m,n$), any non-negative solution $(u,v)$ of the system is bounded by a constant independent of $(u,v)$. Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary.\n  The case $m=1$ was considered by Souplet "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0412","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"}