This article is cited in 1 paper

Necessary and Sufficient Conditions for the Existence and $\varepsilon$-Uniqueness of Bounded Solutions of the Equation $x'=f(x)-h(t)$

V. E. Slyusarchuk

Ukranian State Academy of Water Economy

Abstract: 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.

UDC: 517.988.63

Received: 15.08.2008

DOI: 10.4213/mzm6570

 English version: Mathematical Notes, 2011, 90:1, 136–141

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