Time scale extensions of a theorem of Wintner on systems with asymptotic equilibrium


Mert R., Zafer A.

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, vol.17, no.5, pp.841-857, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 5
  • Publication Date: 2011
  • Doi Number: 10.1080/10236191003639459
  • Journal Name: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.841-857

Abstract

We consider quasilinear dynamic systems of the form[image omitted]where is a time scale, and provide extensions of a theorem of Wintner on systems with asymptotic equilibrium to arbitrary time scales. More specifically, we give sufficient conditions for the asymptotic equilibrium of the above system in the sense that for any given constant vector c, there is a solution satisfying[image omitted] Our results are new for difference equations, q-difference equations and many other time scale systems even though their analogous for differential equations have been known for some time.