Necessary and sufficient conditions for the invertibility of the nonlinear difference operator \(({\mathcal D}x)(t)= x(t+1)- f(x(t))\) in the space of bounded continuous functions on the real axis (Q2759310)
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scientific article; zbMATH DE number 1681714
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient conditions for the invertibility of the nonlinear difference operator \(({\mathcal D}x)(t)= x(t+1)- f(x(t))\) in the space of bounded continuous functions on the real axis |
scientific article; zbMATH DE number 1681714 |
Statements
3 January 2002
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difference operator
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non-linear operator
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invertibility
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Necessary and sufficient conditions for the invertibility of the nonlinear difference operator \(({\mathcal D}x)(t)= x(t+1)- f(x(t))\) in the space of bounded continuous functions on the real axis (English)
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A nonlinear difference operator of the form \(({\mathcal D}x)(t)=x(t+1)-f(x(t)),\) \(t\in \mathbb{R},\) on the space of bounded continuous functions on the real line is studied. Necessary and sufficient conditions for the invertibility of this operator in terms of the function \(f\) are given.
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