Annali di Matematica Pura ed Applicata

, Volume 188, Issue 4, pp 543–559

Existence results for periodic solutions of integro-dynamic equations on time scales

Article

DOI: 10.1007/s10231-008-0088-z

Cite this article as:
Adıvar, M. & Raffoul, Y.N. Annali di Matematica (2009) 188: 543. doi:10.1007/s10231-008-0088-z

Abstract

Using 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)

Keywords

Periodic time scaleDynamic equationVolterra integral equationSobolev’s inequalitySchaeferLyapunovPeriodic solution

Mathematics Subject Classification (2000)

45G1545D0534A1234A34

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsIzmir University of EconomicsIzmirTurkey
  2. 2.Department of MathematicsUniversity of DaytonDaytonUSA