{"paper":{"title":"Positive subharmonic solutions to superlinear ODEs with indefinite weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guglielmo Feltrin","submitted_at":"2017-01-22T10:00:02Z","abstract_excerpt":"We study the positive subharmonic solutions to the second order nonlinear ordinary differential equation \\begin{equation*} u'' + q(t) g(u) = 0, \\end{equation*} where $g(u)$ has superlinear growth both at zero and at infinity, and $q(t)$ is a $T$-periodic sign-changing weight. Under the sharp mean value condition $\\int_{0}^{T} q(t) ~\\!dt < 0$, combining Mawhin's coincidence degree theory with the Poincar\\'e-Birkhoff fixed point theorem, we prove that there exist positive subharmonic solutions of order $k$ for any large integer $k$. Moreover, when the negative part of $q(t)$ is sufficiently larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06145","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"}