From the introduction: In this study, we are concerned with determining the eigenvalue intervals of \(\lambda_i\), \(1\leq i\leq n\), for which there exist positive solutions for the iterative system of nonlinear boundary value problems with integral boundary conditions on time scales, \[ \begin{gathered} u^{\Delta\Delta}_i(t)+ \lambda_i q_i(t) f_i(u_{i+1}(t))= 0,\quad t\in [0,1]_{\mathbb{T}},\;1\leq i\leq n,\\ u_{n+1}(t)= u_1(t),\quad t\in [0,1]_{\mathbb{T}},\end{gathered} \] satisfying the integral boundary conditions, \[ \begin{aligned} au_i(0)-bu^\Delta_i(0) &= \int^1_0 g_1(t) u_i(t)\Delta at,\\ cu_i(1)+ du^\Delta_i(1) &= \int^1_0 g_2(t)u_i(t)\Delta t,\quad 1\leq i\leq n,\end{aligned} \] where \(\mathbb{T}\) is a time scale, \(0,1\in\mathbb{T}\), \([0,1]_{\mathbb{T}}= [0,1]\cap\mathbb{T}\).