Ukrainian Mathematical Journal

, Volume 49, Issue 7, pp 1089–1101 | Cite as

Nonlinear difference equations with asymptotically stable solutions

  • V. E. Slyusarchuk
Article
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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.

Keywords

Banach Space Difference Equation Asymptotic Stability Trivial Solution Spectral Radius 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. E. Slyusarchuk

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