{"paper":{"title":"Slowly growing solutions of ODEs revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Janne Gr\\\"ohn","submitted_at":"2017-07-31T08:37:32Z","abstract_excerpt":"Solutions of the differential equation $f''+Af=0$ are considered assuming that $A$ is analytic in the unit disc $\\mathbb{D}$ and satisfies \\begin{equation} \\label{eq:dag} \\sup_{z\\in\\mathbb{D}} \\, |A(z)| (1-|z|^2)^2 \\log\\frac{e}{1-|z|} < \\infty. \\tag{$\\star$} \\end{equation} By recent results in the literature, such restriction has been associated to coefficient conditions which place all solutions in the Bloch space $\\mathcal{B}$. In this paper it is shown that any coefficient condition implying \\eqref{eq:dag} fails to detect certain cases when Bloch solutions do appear. The converse problem is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09760","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"}