{"paper":{"title":"Classification of solutions to $3$-D and $4$-D mixed order conformally invariant systems with critical and exponential growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lixiu Duan, Rong Zhang, Wei Dai","submitted_at":"2024-01-08T16:16:55Z","abstract_excerpt":"In this paper, without any assumption on $v$ and under the extremely mild assumption $u(x)= O(|x|^{K})$ as $|x|\\rightarrow+\\infty$ for some $K\\gg1$ arbitrarily large, we classify solutions of the following conformally invariant system with mixed order and exponentially increasing nonlinearity in $\\mathbb{R}^{3}$: $$ \\begin{cases} \\ (-\\Delta)^{\\frac{1}{2}} u=v^{4} ,&x\\in \\mathbb{R}^{3},\\\\ \\ -\\Delta v=e^{pw} ,&x\\in \\mathbb{R}^{3},\\\\ \\ (-\\Delta)^{\\frac{3}{2}} w=u^{3} ,&x\\in \\mathbb{R}^{3}, \\end{cases} $$ where $p>0$, $w(x)=o(|x|^{2})$ at $\\infty$ and $u,v\\geq0$ satisfies the finite total curvatur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03994","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.03994/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}