Geodesic
Asymptotic instability of nonlinear differential equations
Electronic Journal of Differential Equations, Tome 1997 (1997).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {1997},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a11/}
}
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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/