Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 16, pp 1-7.

Title:  Asymptotic instability of nonlinear differential equations
 
Authors: Rafael Avis (Univ. de Oriente, Cumana, Venezuela)
 Raul Naulin (Univ. de Oriente, Cumana, Venezuela)

Abstract: 
 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-Pint\'er, and  K.  L.  Chiou.

Submitted July 9, 1997. Published October 15, 1997.
Math Subject Classification:39A11, 39A10.   
Key Words: Liapunov instability; h-stability.