Electron. J. Diff. Eqns., Vol. 1997(1997), No. 16, pp 1-7.

Asymptotic instability of nonlinear differential equations

Rafael Avis & Raul Naulin

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-Pinter, and K. L. Chiou.

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

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Rafael Avis & Raul Naulin
Departamento de Matematicas, Universidad de Oriente, Cumana 6101 A-285. Venezuela
e-mail: rnaulin@cumana.sucre.udo.edu.ve
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