Adıvar, MuratRaffoul, Youssef N.2023-06-162023-06-1620090373-31141618-1891https://doi.org/10.1007/s10231-008-0088-zhttps://hdl.handle.net/20.500.14365/879Using the topological degree method and Schaefer's fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. Furthermore, we provide several applications to scalar equations, in which we develop a time scale analog of Lyapunov's direct method and prove an analog of Sobolev's inequality on time scales to arrive at a priori bound on all periodic solutions. Therefore, we improve and generalize the corresponding results in Burton et al. (Ann Mat Pura Appl 161: 271-283, 1992)eninfo:eu-repo/semantics/closedAccessPeriodic time scaleDynamic equationVolterra integral equationSobolev's inequalitySchaeferLyapunovPeriodic solutionArticle10.1007/s10231-008-0088-z2-s2.0-70349652161