Eigenvalue intervals for iterative systems of nonlinear boundary value problems on time scales

Values of λ1, λ2, · · · , λn are determined for which there exist positive solutions of the iterative system of dynamic equations, u∆∆ i (t) + λiai(t)fi(ui+1(σ(t))) = 0, 1 ≤ i ≤ n, un+1(t) = u1(t), for t ∈ [a, b]T, and satisfying the boundary conditions, αui(a) − βu∆ i (a) = 0 = γui(σ 2 (b)) + δu∆ i (σ(b)), 1 ≤ i ≤ n, where T is a time scale. A Guo-Krasnosel’skii fixed point theorem is applied.