Abstract
We show that if the Lyapunov exponents associated to a linear equation $x'=A(t)x$ are equal to the given limits, then this asymptotic behavior can be reproduced by the solutions of the nonlinear equation $x'=A(t)x+f(t, x)$ for any sufficiently small perturbation $f$. We consider the linear equation with a very general nonuniform behavior which has different growth rates.
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