On the Asymptotic Behavior of Solutions of Differential Systems - Pham, Van Viet; Vu, Tuan (Ukrains’kyi Matematychnyi Zhurnal, 2005)
There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions. Let ϕ (t) be a scalar continuous monotonically increasing positive function tending to ∞ as t → ∞. It is established that if all solutions of a differential system satisfy the inequality \| x(t;t_0 , x_0 ) \| Mφ (t_0 ) φ (t) for allt t_0 ,x_0 { x:\| x \| α }, then the solution x(t; t_0, x_0) of this differential system tends to 0 faster than Mφ (t_0 ) φ (t) .