STABILITY IN TOTALLY NONLINEAR NEUTRAL DYNAMIC EQUATIONS ON TIME SCALES

Let U be a time scale which is unbounded above and below and such that 0 is an element of T. Let id - tau : [0, infinity) boolean AND T -> T be such that (id - tau) ([0, infinity) boolean AND T) is a time scale. We use the Krasnoselskii-Burton's fixed point theorem to obtain stability results about the zero solution for the following totally nonlinear neutral dynamic equation with variable delay x(Delta)(t) = -a (t) h (x(sigma) (t)) + c (t) x (Delta) over tilde (t - tau (t)) + b (t) G (x (t), x (t - T (t)), t is an element of [0, infinity) boolean AND T, where f(Delta) A is the Delta-derivative on U and f (Delta) over tilde is the Delta-derivative on (id - tau) (T). The results obtained here extend the work of Ardjouni, Derrardjia and Djoudi [2].