Asymptotic Discontinuity of Smooth Solutions of Nonlinear $q$-Difference Equations

• Date: 2000
• Main Authors: Derfel', G. A., Romanenko, Ye. Yu., Sharkovsky, O. M., Дерфель, Г. А., Романенко, Е. Ю., Шарковский, А. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4566
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the asymptotic behavior of solutions of the simplest nonlinear q-difference equations having the form x(qt+ 1) = f(x(t)), q> 1, t∈ R +. The study is based on a comparison of these equations with the difference equations x(t+ 1) = f(x(t)), t∈ R +. It is shown that, for “not very...