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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2011_90_1_a11,
     author = {V. E. Slyusarchuk},
     title = {Necessary and {Sufficient} {Conditions} for the {Existence} and $\varepsilon${-Uniqueness} of {Bounded} {Solutions} of the {Equation} $x'=f(x)-h(t)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {137--142},
     publisher = {mathdoc},
     volume = {90},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a11/}
}
TY  - JOUR
AU  - V. E. Slyusarchuk
TI  - Necessary and Sufficient Conditions for the Existence and $\varepsilon$-Uniqueness of Bounded Solutions of the Equation $x'=f(x)-h(t)$
JO  - Matematičeskie zametki
PY  - 2011
SP  - 137
EP  - 142
VL  - 90
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a11/
LA  - ru
ID  - MZM_2011_90_1_a11
ER  - 
%0 Journal Article
%A V. E. Slyusarchuk
%T Necessary and Sufficient Conditions for the Existence and $\varepsilon$-Uniqueness of Bounded Solutions of the Equation $x'=f(x)-h(t)$
%J Matematičeskie zametki
%D 2011
%P 137-142
%V 90
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a11/
%G ru
%F MZM_2011_90_1_a11
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/