Existence of nonoscillatory solutions to neutral dynamic equations on time scales

In this paper, we give an analogue of the Arzela–Ascoli theorem on time scales. Then, we establish the existence of nonoscillatory solutions to the neutral dynamic equation Δ[x(t)+p(t)x(g(t))]+f(t,x(h(t)))=0 on a time scale. To dwell upon the importance of our results, three interesting examples are also included.