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

Mazanik, S. A.

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 \(t\to \infty\).

Reviewer: V.Chernyatin (Szczecin)

MSC:

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

Keywords:

diagonal system; asymptotic equivalence; perturbations