{"paper":{"title":"Precise asymptotic estimates and non-degeneracy of solutions to a biharmonic problem with large exponents in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenjie Wang, Xiuda Liang","submitted_at":"2026-05-23T01:47:13Z","abstract_excerpt":"We are concerned with the semilinear biharmonic problem under Dirichlet boundary conditions that \\begin{equation*} \\begin{cases} \\Delta^2 u=(u^+)^{p} &{\\text{in}~\\Omega},\\\\[0.5mm] u \\not\\equiv 0 &{\\text{in}~\\Omega},\\\\[0.5mm] u=\\partial u / \\partial \\nu = 0 &{\\text{on}~\\partial \\Omega}, \\end{cases} \\end{equation*} where $\\Omega \\subset \\mathbb{R}^4$ is a smooth bounded domain and $p>1$ is sufficiently large.\n  The basic asymptotic behavior and concentration phenomena of the solutions for this problem have been established in literatures. In this work, we aim to refine some known asymptotic esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24338","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24338/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"}