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Asymptotic equivalence under perturbations of diagonal systems. (English. Russian original) Zbl 0824.34059

Differ. Equations 30, No. 4, 675 (1994); translation from Differ. Uravn. 30, No. 4, 728 (1994).
[Summary of an article deposited at VINITI (Moscow) under No. 2505- B93.]
The author shows the class of perturbations \(Q(t)\) under which the perturbed differential system \(Dx= [A(t)+ Q(t)]x\) is asymptotically equivalent to the original diagonal one \(Dx= A(t)x\) in the sense of convergence of their solutions for \(t\to \infty\).

MSC:

34D10 Perturbations of ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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