{"paper":{"title":"Existence of periodic solutions in shifts $\\delta_{\\pm}$ for neutral nonlinear dynamic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Can Koyuncuoglu, Murat Adivar, Youssef N. Raffoul","submitted_at":"2014-02-11T16:01:23Z","abstract_excerpt":"In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \\[ x^{\\Delta}(t)=A(t)x(t)+Q^{\\Delta}\\left(t,x\\left(\\delta_{-}(s,t)\\right) \\right) +G\\left(t,x(t),x\\left(\\delta_{-}(s,t)\\right) \\right) . \\] We utilize the new periodicity concept in terms of shifts operators, which allows us to extend the concept of periodicity to time scales where the additivity requirement $t\\pm T\\in\\mathbb{T}$ for all $t\\in\\mathbb{T}$ and for a fixed $T>0,$ may not hold. More, importantly, the new concept will easily handle time scales that are not periodic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2540","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"}