Behavior of solutions of impulsively perturbed non-halflinear oscillator equations

Intermittently and instantaneously perturbed oscillator equations play an i mportant role in theory and application. In this paper, we investigate the asymptotic behavior of solutions of the impulsive system (phi(beta)(x')Y f(x) = 0 for t not equal t(n), x'(t(n) + 0) = b(n)x'(t(n)), where n = 1, 2, ..., and phi(beta)(u) = \ u \(beta) sgn u for beta > 0. In the special case f(u) = phi(beta)(u), we obtain the so-called half-linear system, which exh ibits similar behavior to the linear case. First, we prove attractivity res ults, and then apply our theorems to the nonautonomous equation (phi(beta)( x')Y + q(t)f(x) = 0, where q(t) is a step-function. (C) 2000 Academic Press .