We establish some necessary conditions on the nonoscillation of the following half-linear second order differential equation [r(t)\u'(t)\(p-2) u'(t)]' + C(t)\u(t)\(P-2) u(t) = 0, t greater than or equal to t(0), where p > 1 is a constant, r(t) and c(t) are continuous functions from [t(0), infinity) to [0, infinity) with r(t) > 0.
