{"paper":{"title":"Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shuangjie Peng, Shusen Yan, Yuxia Guo","submitted_at":"2015-03-22T11:38:15Z","abstract_excerpt":"\\begin{abstract} We consider the following poly-harmonic equations with critical exponents: \\begin{equation}\\label{P} (-\\Delta)^m u =K(y)u^{\\frac{N+2m}{N-2m}},\\;\\;\\; u>0\\;\\;\\;\\hbox{in} \\mathbb{R}^N, \\end{equation} where $N> 2m+2,m\\in\\mathbb{N}_{+}, K(y)$ is positive and periodic in its first $k$ variables $(y_1,\\cdots, y_k)$, $1\\leq k<\\frac{N-2m}{2}$. Under some conditions on $K(y)$ near its critical point, we prove not only that problem~\\eqref{P} admits solutions with infinitely many bubbles, but also that the bubbling solutions obtained in our existence result are locally unique. This local "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06412","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"}