Abstract
In this paper we consider a system of k ≥ 3 dynamic equations on time scales such that the first equation has the neutral term $$\begin{cases}(x_1(t)+p(t)x_1(v(t)))^\Delta=a_1(t)f_1(x_2(u_1(t))),\\{x_i^\Delta}(t)=a_i(t)f_i(x_{i+1}(u_i(t))), & i=2,\ldots,k-1,\\{x_k^\Delta}(t)=a_k(t)f_k(x_1(u_k(t))), & t \in \mathbb{T}.\end{cases}$$ Our purpose is to present sufficient conditions for the existence of eventually positive bounded solutions of the considered system for 1 <α ≤ p(t) ≤ β. The main idea is to apply Krasnoselskii’s fixed point theorem.
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