{"paper":{"title":"Entire solutions of quasilinear symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Mostafa Fazly","submitted_at":"2015-06-08T23:49:17Z","abstract_excerpt":"We study the following quasilinear elliptic system for all $i=1,\\cdots,m$ \\begin{equation*} \\label{}\n  -div(\\Phi'(|\\nabla u_i|^2) \\nabla u_i) = H_i(u) \\quad \\text{in} \\ \\ \\mathbb{R}^n\n  \\end{equation*} where $u=(u_i)_{i=1}^m: \\mathbb R^n\\to \\mathbb R^m$ and the nonlinearity $ H_i(u) \\in C^1(\\mathbb R^m)\\to \\mathbb R$ is a general nonlinearity. Several celebrated operators such as the prescribed mean curvature, the Laplacian and the $p$-Laplacian operators fit in the above form, for appropriate $\\Phi$. We establish a Hamiltonian identity of the following form for all $x_n\\in\\mathbb R$ \\begin{eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02731","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"}