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Let T ⊂ R be a periodic time scale in shifts δ ± associated with the initial point t 0 ∈ T *. We use Brouwer's fixed point theorem to show that the initial value problem x ∆ (t) = p(t)x(t) + q(t), t ∈ T, x(t 0) = x 0 has a periodic solution in shifts δ ±. We extend and unify periodic differential, difference, h-difference and especially q-difference(More)
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