Nonlinear difference equations with asymptotically stable solutions

被引：0

作者：

V. E. Slyusarchuk

机构：

来源：

Ukrainian Mathematical Journal | 1997年 / 49卷 / 7期

关键词：

Banach Space; Difference Equation; Asymptotic Stability; Trivial Solution; Spectral Radius;

D O I：

10.1007/BF02528754

中图分类号：

学科分类号：

摘要：

We establish conditions of asymptotic stability for all solutions of the equation Xn+1=F(Xn), 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.

引用

页码：1089 / 1101

页数：12

共 5 条

[1] Slyusarchuk V. E.(1976)Difference equations in a Banach space Latv. Mat. Ezhegodnik 17 214-229
[2] Tsar'kov E. F.(1983)New theorems on the instability of difference systems with respect to the first approximation Differents. Uravn. 19 906-908
[3] Slyusarchuk V. E.(1986)On the instability of difference equations with respect to the first approximation Differents. Uravn. 22 722-723
[4] Slyusarchuk V. E.(1980)Universal behavior in nonlinear systems Los Alamos Science 1 4-27
[5] Feigenbaum M. J.(undefined)undefined undefined undefined undefined-undefined

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