{"paper":{"title":"Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fabio Zanolin, Guglielmo Feltrin","submitted_at":"2015-08-08T08:02:51Z","abstract_excerpt":"We study the periodic boundary value problem associated with the second order nonlinear differential equation $$ u\" + c u' + \\left(a^{+}(t) - \\mu \\, a^{-}(t)\\right) g(u) = 0, $$ where $g(u)$ has superlinear growth at zero and at infinity, $a(t)$ is a periodic sign-changing weight, $c\\in\\mathbb{R}$ and $\\mu>0$ is a real parameter. We prove the existence of $2^{m}-1$ positive solutions when $a(t)$ has $m$ positive humps separated by $m$ negative ones (in a periodicity interval) and $\\mu$ is sufficiently large. The proof is based on the extension of Mawhin's coincidence degree defined in open (po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01867","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"}