Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation. (16th August 2022) - Wei, Jia; Han, Xiaoling; Ye, Fumei
Abstract : We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ 4 u k − 2 − a k u α k + b k u β k = 0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δ u k = u k + 1 − u k is the forward difference operator, α > 0, β > 0 and α ≠ β, a k, b k are T -periodic functions and a k b k > 0 . As applications, we give some examples to illustrate the application of these theorems.