{"paper":{"title":"Positive subharmonic solutions to nonlinear ODEs with indefinite weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Guglielmo Feltrin","submitted_at":"2016-05-09T10:00:01Z","abstract_excerpt":"We prove that the superlinear indefinite equation \\begin{equation*} u\" + a(t)u^{p} = 0, \\end{equation*} where $p > 1$ and $a(t)$ is a $T$-periodic sign-changing function satisfying the (sharp) mean value condition $\\int_{0}^{T} a(t)~\\!dt < 0$, has positive subharmonic solutions of order $k$ for any large integer $k$, thus providing a further contribution to a problem raised by G. J. Butler in its pioneering paper (JDE, 1976). The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar\\'e-Birkhof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02500","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"}