Geodesic
Bounded solutions of linear almost periodic differential equations
Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 581-600

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

The paper deals with bounded (on $\mathbb R_+$ or $\mathbb R$) solutions of the equation $\dot x=\mathcal A(t)x$ with recurrent (almost periodic) coefficients. We show that the zero solution of this equation is uniformly stable (bistable) if and only if all its solutions and the solutions of its limit equations are bounded on $\mathbb R_+$ ($\mathbb R$). These results are generalizations of the well-known theorem of Cameron–Johnson. 
@article{IM2_1998_62_3_a5,
     author = {D. N. Cheban},
     title = {Bounded solutions of linear almost periodic differential equations},
     journal = {Izvestiya. Mathematics },
     pages = {581--600},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a5/}
}
TY  - JOUR
AU  - D. N. Cheban
TI  - Bounded solutions of linear almost periodic differential equations
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 581
EP  - 600
VL  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a5/
LA  - en
ID  - IM2_1998_62_3_a5
ER  - 
%0 Journal Article
%A D. N. Cheban
%T Bounded solutions of linear almost periodic differential equations
%J Izvestiya. Mathematics 
%D 1998
%P 581-600
%V 62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a5/
%G en
%F IM2_1998_62_3_a5
D. N. Cheban. Bounded solutions of linear almost periodic differential equations. Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 581-600. http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a5/