Nonlinear difference equations with asymptotically stable solutions

  • V. E. Slyusarchuk

Abstract

We establish conditions of asymptotic stability for all solutions of the equation X n+1=F(X n ), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given.
Published
25.07.1997
How to Cite
SlyusarchukV. E. “Nonlinear Difference Equations With Asymptotically Stable Solutions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 7, July 1997, pp. 970–980. July, https://umj.imath.kiev.ua/index.php/umj/article/view/5088.
Section
Research articles