This article presents new oscillation criteria for the second-order delay differential equation (p(t)(x′(t))alpha)′+q(t)xalpha(t−au)+sumi=1n​qi​(t)xalphai​(t−au)=e(t) where augeq0, p(t)inC1[0,infty), q(t),qi​(t),e(t)inC[0,infty), p(t)>0, alpha1​>dots>alpham​>alpha>alpham+1​>dots>alphan​>0(n>mgeq1), alpha1​,dots,alphan​ and alpha are ratio of odd positive integers. Without assuming that q(t),qi​(t) and e(t) are nonnegative, the results in [6,8] have been extended and a mistake in the proof of the results in [3] is corrected