EXISTENCE OF PERIODIC SOLUTIONS OF TOTALLY NONLINEAR NEUTRAL DYNAMIC EQUATIONS WITH FUNCTIONAL DELAY ON A TIME SCALE

摘要

Let T be a periodic time scale. Using a modification of Krasnoselskii's fixed point theorem due to Burton, we show that the totally nonlinear dynamic equation with functional delay x~△(t) = ?a (t) h (x~σ (t)) + c(t)Q~△(x (t ? r (t))) + G(t, x (t) , x (t ? r (t))) ,where t ∈ T, f~△ is the △-derivative on T and f~△ is the △-derivative on (id ? r) (T), has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the Burton-Krasnoselskii's theorem. The results obtained here extend the results in the literature.