{"paper":{"title":"Radial symmetry of positive entire solutions of a fourth order elliptic equation with a singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Long Wei, Zongming Guo","submitted_at":"2018-04-23T01:29:25Z","abstract_excerpt":"The necessary and sufficient conditions for a regular positive entire solution $u$ of the biharmonic equation: \\begin{equation} \\label{0.1} -\\Delta^2 u=u^{-p} \\;\\; \\mbox{in $\\R^N \\; (N \\geq 3)$}, \\;\\; p>1 \\end{equation} to be a radially symmetric solution are obtained via the moving plane method (MPM) of a system of equations. It is well-known that for any $a>0$, \\eqref{0.1} admits a unique minimal positive entire radial solution ${\\underline u}_a (r)$ and a family of non-minimal positive entire radial solutions $u_a (r)$ such that $u_a (0)={\\underline u}_a (0)=a$ and $u_a (r) \\geq {\\underline"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08215","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"}