On properties of nonlinear second order systems under nonlinear impulse perturbations

In this paper, we consider the impulsive second order system [ ddot{x}+f(x)=0quad (teq t_{n});quad dot{x}(t_{n}+0)=b_{n}dot{x}(t_{n}) quad (t=t_{n}) ] where $t_n=t_0+n,p$ $(p>0, n=1,2dots )$. In a previous paper, the authors proved that if $f(x)$ is strictly nonlinear, then this system has infinitely many periodic solutions. The impulses account for the main differences in the attractivity properties of the zero solution. Here, we prove that these periodic solutions are attractive in some sense, and we give good estimates for the attractivity region.