Applications of Conley index theory on difference equations with non-resonance. (October 2020)

• Record Type: Journal Article
• Authors: Zhou, Ben-Xing; Liu, Chungen
• Is Part Of: Applied mathematics letters. Volume 108(2020)
• Publication Date: 2020-10
• Subjects: Difference equations -- Periodic solutions -- Conley index -- Morse index; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106500
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Inspired by Chang (1981) and Long (1990), we consider the existence of periodic solutions for second-order difference equations with asymptotically linear nonlinearity via Conley index theory. Moreover, when we study the following one-dimensional autonomous difference equations with form Δ 2 x n − 1 + f ( x n ) = 0, n ∈ Z, x n ∈ R, we can derive at least three periodic solutions under suitable assumptions.