The oscillation and asymptotically monotone solutions of second-order quasilinear differential equations

Abstract

We offer sufficient conditions for the oscillation of all solutions of the perturbed quasilinear differential equation (a(t)|y′|α-1y′)′ + Q(t, y) = P(t, y, y′) as well as for the existence of a positive monotone solution of the damped differential equation (a(t)|y′|α-1y′)′ + b(t)|y′\α-1y′ + H(t, y) = 0, where α > 0. Examples that dwell upon the importance of our results are also included. © Elsevier Science Inc., 1996.