{"paper":{"title":"Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Calin Serban, Jean Mawhin, Petru Jebelean","submitted_at":"2025-06-05T12:01:10Z","abstract_excerpt":"We are concerned with the existence of $T$-periodic solutions to an equation of type $$\\left (|u'(t))|^{p(t)-2} u'(t) \\right )'+f(u(t))u'(t)+g(u(t))=h(t)\\quad \\mbox{ in }[0,T]$$ where $p:[0,T]\\to(1,\\infty)$ with $p(0)=p(T)$ and $h$ are continuous on $[0,T]$, $f,g$ are also continuous on $[0,\\infty)$, respectively $(0,\\infty)$. The mapping $g$ may have an attractive singularity (i.e. $g(x) \\to +\\infty$ as $x\\to 0+$). Our approach relies on a continuation theorem obtained in the recent paper M. Garc\\'{i}a-Huidobro, R. Man\\'{a}sevich, J. Mawhin and S. Tanaka, J. Differential Equations (2024), a p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04927","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04927/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}