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In this paper, we establish the existence of nonoscillatory solutions to the neutral dynamic equation x(t)-b a p(t, η)x(g(t, η)) η + d c ω(t, ν)x(h(t, ν)) ν = 0 on a time scale T. Some examples are given to illustrate the main results.

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We will discuss nonoscillatory solutions to the n-dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the property limt→∞ ⁡x i(t) = 0, i = 1, 2,…, n.