Bounded Solutions of a Triangular System of Two Nonlinear Discrete Equations

A nonlinear triangular system of discrete equations u_1(k + 1) = q_1(k)u^p_1 (k), u_2(k + 1) = q_2(k)u^r_1(k)u^t_2(k) is considered where q_i: {a, a + 1,...} → (0, ∞), i = 1, 2 are given functions, a is a fixed positive integer and p, r, t are positive numbers. Sufficient conditions are given for the existence of a solution u = (u_1, u_2): {a, a + 1,...} → R × R such that its coordinates u_i, i = 1, 2 are between two given functions b_i, c_i: {a, a + 1,...} → R satisfying 0 ≤ b_i(k) < c_i(k) for every k ∈ {a, a + 1,...}.