Geodesic
On the asymptotic behaviour of nonlinear systems of ordinary differential equations
Glasgow mathematical journal, Tome 26 (1985) no. 2, pp. 161-170

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases. For the perturbed systems (P) and (P1) the above property concerning the solutions near zero may or may not remain true. A more precise formulation of this problem is as follows: if zero is stable or asymptotically stable for (N), and if the functions g(t, x) and h(t, x) are small in some sense, give conditions on f(t, x) so that zero is (eventually) stable or asymptotically stable for (P) and (P1). 
Athanassov, Zhivko S. On the asymptotic behaviour of nonlinear systems of ordinary differential equations. Glasgow mathematical journal, Tome 26 (1985) no. 2, pp. 161-170. doi: 10.1017/S0017089500005942
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