{"paper":{"title":"Global Compactness and Existence for Higher Order Critical Equations on Hyperbolic Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jungang Li, Zhiwei Wang","submitted_at":"2024-11-22T04:16:56Z","abstract_excerpt":"We study the higher-order Schr\\\"odinger equation with critical Sobolev exponent on the hyperbolic space $\\mathbb{H}^n$: $$P_m u + a(x)\\,u = |u|^{q-2}u, \\quad u \\in D^{m,2}(\\mathbb{H}^n),$$ where $P_m$ is the GJMS operator of order $2m$, $q = \\frac{2n}{n-2m}$ is the critical exponent, and $a(x) \\geq 0$ is a potential in $L^{n/2m}(\\mathbb{H}^n)$. This problem simultaneously generalizes the classical work of Benci--Cerami from second-order to arbitrary order and from Euclidean space to hyperbolic space.\n  We establish a global compactness theorem (profile decomposition) for Palais--Smale sequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14719","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/2411.14719/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"}