Asymptotic behavior of solutions of perturbed linear systems

Bobisud, L. E.

doi:10.1090/S0002-9939-1972-0301313-7

Asymptotic behavior of solutions of perturbed linear systems
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by L. E. Bobisud PDF

Proc. Amer. Math. Soc. 35 (1972), 457-463 Request permission

Abstract:

The existence of solutions of the system $y’ + Ay = f(t,y)$ having the form $y(t) = Z(t)a(t)$ is proved, where $Z(t)$ satisfies $Z’ + AZ = 0$ and the vector $a(t)$ has limit $\alpha$ as t increases. Estimates for the rate of convergence to zero of $a(t) - \alpha$ and of $y(t) - Z(t)\alpha$ are obtained.

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