On a Class of Nonautonomous Max-Type Difference Equations. (18th August 2011)

• Record Type: Journal Article
• Authors: Liu, Wanping; Yang, Xiaofan; Stević, Stevo
• Other Names: N'Guerekata Gaston Mandata Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-08-18
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/436852
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper addresses the max-type difference equationx n = max { f n / x n − k α, B / x n − m β }, n ∈ ℕ 0, wherek, m ∈ ℕ, B > 0, and( f n ) n ∈ ℕ 0 is a positive sequence with a finite limit. We prove that every positive solution to the equation converges tomax { ( lim n → ∞ f n ) 1 / ( α + 1 ), B 1 / ( β + 1 ) } under some conditions. Explicit positive solutions to two particular cases are also presented.