EXISTENCE, UNIQUENESS AND POSITIVITY OF SOLUTIONS FOR A NEUTRAL NONLINEAR PERIODIC DYNAMIC EQUATION ON A TIME SCALE - Ardjouni, A.; Djoudi, A. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2016)
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^(t) =-a(t)x(t)+(Q(t,x(g(t))))^+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.