Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation. (16th August 2022)

• Record Type: Journal Article
• Authors: Wei, Jia; Han, Xiaoling; Ye, Fumei
• Other Names: Avery Richard I. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-08-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/1830248
• Languages: English
• ISSNs: 2314-8896

Abstract

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.