STABILITY IN NEUTRAL NONLINEAR DYNAMIC EQUATIONS ON A TIME SCALE WITH FUNCTIONAL DELAY

Let T be a time scale that is unbounded above and below and such that 0 ∈ T. Let τ : T → T be such that τ (T) is a time scale. We use fixed point theorems to obtain stability results about the zero solution of the nonlinear neutral dynamic equation with functional delay

                                              x^∆(t) = −a(t) x^σ(t) + c(t) x^∆˜( τ (t) ) + q( x(t), x( τ (t)) ) ,   t ∈ T,

where f^∆ is the ∆-derivative on T and f^∆˜ is the ∆-derivative on τ (T).