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Morchało, Jarosław

Asymptotic equivalence of difference equations. (English) Zbl 0942.39001

Math. Slovaca 48, No. 1, 57-68 (1998).
By means of the contraction mapping principle, an asymptotic equivalence is studied between the solutions of a finite-dimensional linear difference equation \(y(n+1)=A(n)y(n)\) and its nonlinear perturbation \(x({n+1})=A(n)x(n)+F\bigl (n,x(n),Tx(n)\bigr)\). Under certain conditions on these equations, a homeomorphism is shown between the sets of bounded solutions of the above equations.
Reviewer: Michal Fečkan (Bratislava)

Cited in 2 Documents

MSC:

39A10 Additive difference equations

Keywords:

difference equations; asymptotic equivalence; bounded solutions; matrix functions
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\textit{J. Morchało}, Math. Slovaca 48, No. 1, 57--68 (1998; Zbl 0942.39001)
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References:

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