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

摘要

In the paper the second order half-linear delay differential equation(r(t)|u′(t)|α-1u′(t))′+p(t)|u(τ(t))|α-1u(τ(t))=0,α>1is studied under the condition ∫∞r-1/α(t)dt<∞. 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 ρ 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.