BOUNDEDNESS IN NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t_∞-SIMILARITY

Abstract

Abstract. This paper shows that the solutions to nonlinear perturbed differential systemhave bounded properties. To show the bounded properties, we impose conditions on the perturbed part t t0 g(s, y(s))ds, h(t, y(t), T y(t)), and on the fundamental matrix of the unperturbed system y = f (t, y) using the notion of h-stability.