Asymptotic discontinuity of smooth solutions of nonlinear q-difference equations

G. A. Derfel, E. Yu Romanenko, A. N. Sharkovsky

Research output: Contribution to journalArticlepeer-review


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 large" q>1, the solutions of the q-difference equation inherit the asymptotic properties of the solutions of the corresponding difference equation; in particular, we obtain an upper bound for the values of the parameter q for which smooth bounded solutions that possess the property max t∈[0,T]|x′(t)|→∞ as T → ∞ and tend to discontinuous upper-semicontinuous functions in the Hausdorff metric for graphs are typical of the q-difference equation.

Original languageEnglish
Pages (from-to)1841-1857
Number of pages17
JournalUkrainian Mathematical Journal
Issue number12
StatePublished - 1 Jan 2000

ASJC Scopus subject areas

  • Mathematics (all)


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