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