Krasnoselskii fixed point theorem and stability results for neutral dynamic equations with variable delays on time scales

  • Belkis Bordj Laboratory of Informatics and Mathematics,\\ Department of Mathematics and Informatics, University of Souk-Ahras,\\ P.O. Box 1553, Souk-Ahras, 41000, Algeria
  • Abdelouaheb Ardjouni Department of Mathematics and Informatics, University of Souk Ahras,\\ P.O. Box 1553, Souk Ahras, 41000, Algeria;Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics,\\ University of Annaba, P.O. Box 12, Annaba 23000, Algeria

Abstract

In this paper, we use Krasnoselskii's fixed point theorem and give sufficient conditions for the boundedness and stability of the zero solution of a neutral dynamic equation with variable delays on time scales. Also weprove a necessary and sufficient condition ensuring the asymptotic stability. The results obtained here extend the work of Benhadri \cite{ben}.

Published
2023-05-19