Remarks on the paper by Sun and Meng, Appl. Math. Comput. 174 (2006)

In the paper the second order half-linear delay differential equation (r(t)vertical bar u '(t)vertical bar(alpha-1) u '(t))' + p(t) vertical bar u(tau(t))vertical bar(alpha-1) u(tau(t)) = 0, alpha > 1 is studied under the condition integral(infinity) r(-1/alpha) (t) dt < infinity. The oscillation criterion proved by Sun and Meng (2006, Theorem 2.2) is carefully examined and improved by simplifying and sharpening the estimates used in the original proof and removing unnecessary assumptions. Among others, using elementary arguments we show that an arbitrary positive nondecreasing function rho from this criterion can be safely and with no loss of generality replaced by a constant function. An extension to other related equations, such as neutral equations is also provided. (C) 2014 Elsevier Inc. All rights reserved.