Geodesic
Asymptotic instability of nonlinear differential equations
Electronic journal of differential equations, Tome 1997 (1997)
This article shows that the zero solution to the system

$ x'=A(t)x+f(t,x),\quad f(t,0)=0 $

is unstable. To show instability, we impose conditions on the nonlinear part $f(t,x)$ and on the fundamental matrix of the linear system $y'=A(t)y$. Our results generalize the instability results obtained by J. M. Bownds, Hatvani-Pinter, and K. L. Chiou.
Classification : 39A11, 39A10
Keywords: Liapunov instability, h-stability 
@article{EJDE_1997__1997__a11,
     author = {Avis,  Rafael and Naulin,  Ra\'ul},
     title = {Asymptotic instability of nonlinear differential equations},
     journal = {Electronic journal of differential equations},
     year = {1997},
     volume = {1997},
     zbl = {0888.34045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a11/}
}
TY  - JOUR
AU  - Avis,  Rafael
AU  - Naulin,  Raúl
TI  - Asymptotic instability of nonlinear differential equations
JO  - Electronic journal of differential equations
PY  - 1997
VL  - 1997
UR  - http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a11/
LA  - en
ID  - EJDE_1997__1997__a11
ER  - 
%0 Journal Article
%A Avis,  Rafael
%A Naulin,  Raúl
%T Asymptotic instability of nonlinear differential equations
%J Electronic journal of differential equations
%D 1997
%V 1997
%U http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a11/
%G en
%F EJDE_1997__1997__a11
Avis,  Rafael; Naulin,  Raúl. Asymptotic instability of nonlinear differential equations. Electronic journal of differential equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a11/