Geodesic
Necessary and Sufficient Conditions for the Existence and $\varepsilon$-Uniqueness of Bounded Solutions of the Equation $x'=f(x)-h(t)$
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 137-142.

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We introduce the notion of $\varepsilon$-unique bounded solution to the nonlinear differential equation $x'=f(x)-h(t)$, where $f\colon\mathbb R\to\mathbb R$ is a continuous function and $h(t)$ is an arbitrary continuous function bounded on $\mathbb R$. We derive necessary and sufficient conditions for the existence and $\varepsilon$-uniqueness of bounded solutions to this equation.
Keywords: nonlinear differential equation, bounded solution, $\varepsilon$-uniqueness, Banach space. 
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     title = {Necessary and {Sufficient} {Conditions} for the {Existence} and $\varepsilon${-Uniqueness} of {Bounded} {Solutions} of the {Equation} $x'=f(x)-h(t)$},
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V. E. Slyusarchuk. Necessary and Sufficient Conditions for the Existence and $\varepsilon$-Uniqueness of Bounded Solutions of the Equation $x'=f(x)-h(t)$. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 137-142. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a11/

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