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)
This work is concerned with the existence of positive solutions to a nonlinear nonlocal first-order multipoint problem. Here the nonlinearity is allowed to take on negative values, not only positive values.