{"paper":{"title":"Time Asymptotic expansions of solution for fourth-order Schr\\\"odinger equation with zero resonance or eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongliang Feng, Xiaohua Yao, Zhao Wu","submitted_at":"2018-12-01T16:28:18Z","abstract_excerpt":"In this paper, we first deduce the asymptotic expansions of resolvent of $H=(-\\Delta)^2+V$ with the presence of resonance or eigenvalue at the degenerate zero threshold for $d\\geq5$. In particular, we identify these resonance spaces for full kinds of zero resonances. As a consequence, we then establish the {\\it time asymptotic expansions} and {\\it Kato-Jensen estimates} for the solution of fourth-order Schr\\\"odinger equation under the presence of zero resonance or eigenvalue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00223","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":""},"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"}