{"paper":{"title":"Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lucas C. F. Ferreira, Marcelo Montenegro, Matheus C. Santos","submitted_at":"2013-07-24T20:50:22Z","abstract_excerpt":"We study the semilinear elliptic equation $\\Delta u + g(x,u,Du) = 0$ in $\\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6578","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"}