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

摘要

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.