{"paper":{"title":"Periodic solutions to parameter-dependent equations with a $\\phi$-Laplacian type operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elisa Sovrano, Fabio Zanolin, Guglielmo Feltrin","submitted_at":"2018-04-02T10:00:02Z","abstract_excerpt":"We study the periodic boundary value problem associated with the $\\phi$-Laplacian equation of the form $(\\phi(u'))'+f(u)u'+g(t,u)=s$, where $s$ is a real parameter, $f$ and $g$ are continuous functions, and $g$ is $T$-periodic in the variable $t$. The interest is in Ambrosetti-Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter $s$. We investigate this problem for a broad family of nonlinearities, under non-uniform type conditions on $g(t,u)$ as $u\\to \\pm\\infty$. We generalize, in a unified framework, various classical and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00439","kind":"arxiv","version":2},"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"}