A criterion for the exponential stability of linear difference equations

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We give an affirmative answer to a question formulated by Aulbach and Van Minh by showing that the linear difference equation xn+1 = A nxn, for n ε ℕ in a Banach space B is exponentially stable if and only if for every f = {fn} n=1ε ∫ lp(ℕ, B), where 1 <p <∞, the solution of the Cauchy problem xn+1 = A nxn + fn, for n ε ℕ, x1 = 0 is bounded on ℕ.

Original language English 779-783 5 Applied Mathematics Letters 17 7 https://doi.org/10.1016/j.aml.2004.06.005 Published - Jul 2004

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Linear Difference Equation
Banach spaces
Difference equations
Exponential Stability
Asymptotic stability
Cauchy Problem
Banach space
If and only if

Keywords

• Difference equations in Banach spaces
• Exponential stability
• L-spaces
• Linear equation

ASJC Scopus subject areas

• Computational Mechanics
• Control and Systems Engineering
• Applied Mathematics
• Numerical Analysis

Cite this

In: Applied Mathematics Letters, Vol. 17, No. 7, 07.2004, p. 779-783.

Research output: Contribution to journalArticle

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