POSITIVE SOLUTIONS FOR ITERATIVE SYSTEMS OF NONLINEAR BOUNDARY VALUE PROBLEMS ON TIME SCALES

Abstract

Values of λ1, λ2, …, λn are determined for which there exist positive solutions of the iterative system of dynamic equations, [Formula: see text], 1 ≤ i ≤ n, un+1(t) = u1(t), for t ∈ [a, b]𝕋, and satisfying the boundary conditions, [Formula: see text], 0 ≤ m ≤ n - 2, ui(σn (b)) = 0, 1 ≤ i ≤ n, where 𝕋 is a time scale. A Guo-Krasnosel'skii fixed point theorem is applied.𝕋