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Necessary and Sufficient Conditions for the Invertibility of the Nonlinear Difference Operator \(\left( {\mathcal{D}x} \right)\left( t \right) = x\left( {t + 1}\right) - f\left( {x\left( t \right)} \right)\) in the Space of Functions Bounded and Continuous on the Axis

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Nonlinear Oscillations

Abstract

We find necessary and sufficient conditions for the nonlinear difference operator \(\left( {\mathcal{D}x} \right)\left( t \right) = x\left( {t + 1} \right) - f\left( {x\left( t \right)} \right)\) \(t \in \mathbb{R}\), where \(f:\mathbb{R} \to \mathbb{R}\) is a continuous function, to have the inverse in the space of functions bounded and continuous on \(\mathbb{R}\).

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  1. Rivne State Technical University, Rivne

    V. E. Slyusarchu

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  1. V. E. Slyusarchu
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Slyusarchu, V.E. Necessary and Sufficient Conditions for the Invertibility of the Nonlinear Difference Operator \(\left( {\mathcal{D}x} \right)\left( t \right) = x\left( {t + 1}\right) - f\left( {x\left( t \right)} \right)\) in the Space of Functions Bounded and Continuous on the Axis. Nonlinear Oscillations 5, 372–378 (2002). https://doi.org/10.1023/A:1022300525477

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