{"paper":{"title":"On oscillation of solutions of linear differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Janne Gr\\\"ohn, Jouni R\\\"atty\\\"a","submitted_at":"2015-05-29T20:05:16Z","abstract_excerpt":"An interrelationship is found between the accumulation points of zeros of non-trivial solutions of $f\"+Af=0$ and the boundary behavior of the analytic coefficient $A$ in the unit disc $\\mathbb{D}$ of the complex plane $\\mathbb{C}$.\n  It is also shown that the geometric distribution of zeros of any non-trivial solution of $f\"+Af=0$ is severely restricted if $$\\label{eq:cs_a}\\tag{$\\star$} |A(z)| (1-|z|^2)^2 \\leq 1 + C (1-|z|), \\quad z\\in\\mathbb{D}, $$ for any constant $0<C<\\infty$. These considerations are related to the open problem whether \\eqref{eq:cs_a} implies finite oscillation for all non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00009","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"}