EXISTENCE, UNIQUENESS AND POSITIVITY OF SOLUTIONS FOR A NEUTRAL NONLINEAR PERIODIC DYNAMIC EQUATION ON A TIME SCALE

Authors

  • A. Ardjouni Department of Mathematics and Informatics, Souk Ahras University, Souk Ahras, 41000, Algeria
  • A. Djoudi Department of Mathematics, Annaba University, Annaba, 23000, Algeria

Abstract

Let T be a periodic time scale. We use Krasnoselskii's fixed point theorem, to show new results on the existence and positivity of solutions for the nonlinear periodic dynamic equation with variable delay of the form
$x^{\triangle}(t) =-a(t)x(t)+(Q(t,x(g(t))))^{\triangle}+G(t,x(t),x(g(t)))$,
$x(t+T) =x(t)$.
Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique.

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Published

2016-12-25

How to Cite

Ardjouni, A., & Djoudi, A. (2016). EXISTENCE, UNIQUENESS AND POSITIVITY OF SOLUTIONS FOR A NEUTRAL NONLINEAR PERIODIC DYNAMIC EQUATION ON A TIME SCALE. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 6(2), 19-29. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/362

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Section

Research Article