On the asymptotic behavior of solutions of impulsively damped nonlinear oscillator equations

Intermittently damped oscillator equations are important both in practice and attractivity investigations. The problem of attractivity appears clearly if the damping is concentrated into discrete points. s paper we investigate the asymptotic behavior of the impulsive equation ẍ + ƒ(x) = 0 (t ≠ tn) ẋ(tn + 0) = bnẋ(tn) (t = tn) (n = 1, 2, …). We find an analogy, but not strict correspondence, to the attractivity results for distributed damping. The attractivity properties mainly depend on the properties of f(x).