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Instability of nonautonomous differential systems. (English) Zbl 0992.34034
Summary: The author shows that the existence of an $$(h,k)$$-dichotomy for $$x'=A(t)x$$ yields an analysis of the instability of the null solution to the nonautonomous linear system $$y'=A(t)y+ f(t,y)$$, $$f(t,0)=0$$, where $$x'=A(t)x$$ does not satisfy the conditions of Coppel’s theorem on instability.

MSC:
 34D09 Dichotomy, trichotomy of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations