Abstract
Values of lambda 1, lambda 2, ..., lambda n are determined for which there exist positive solutions of the iterative system of dynamic equations, [formulaomitted]$u_i\Delta(n)}} \,(t)\, + \,\lambda_i a_i (t)f_i (u_{i + 1} (\sigma (t)))\, = \,0$, 1 less than or equal to i less than or equal to n, un+1(t) = u1(t), for t [isin] [a, b]T, and satisfying the boundary conditions, [formulaomitted]$u_i\Delta (m)} } \,(a)\, = \,0$, 0 less than or equal to m less than or equal to n - 2, ui( sigma n (b)) = 0, 1 less than or equal to i less than or equal to n, where T is a time scale. A Guo-Krasnosel'skii fixed point theorem is applied.T