{"paper":{"title":"Symmetry of Solutions for a Fractional System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pei Ma, Yan Li","submitted_at":"2016-04-06T02:15:38Z","abstract_excerpt":"We consider the following equations: \\begin{equation*} \\left\\{\\begin{array}{ll} (-\\triangle)^{\\alpha/2}u(x)=f(v(x)), \\\\ (-\\triangle)^{\\beta/2}v(x)=g(u(x)), &x \\in R^{n},\\\\ u,v\\geq 0, &x \\in R^{n}, \\end{array} \\right. \\end{equation*} for continuous $f, g$ and $\\alpha, \\beta \\in (0,2)$. Under some natural assumptions on $f$ and $g$, by applying the \\emph{method of moving planes} directly to the system, we obtain symmetry on non-negative solutions without any decay assumption on the solutions at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01465","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"}