Sharp explicit oscillation conditions for difference equations with several delays (Q2021434)

This paper deals with a first-order linear difference equation of the form \[ \Delta x(n)+\sum \limits_{k=1}^{m}p_{k}(n)x(\tau _{k}(n))=0,~n\in \mathbb{N}_{0}. \] Explicit sufficient conditions are stated for the oscillation of all solutions. Moreover, three examples are given to show that some tests used in some recent papers and based on the results in [\textit{G. E. Chatzarakis} et al., Aequationes Math. 88, No. 1--2, 105--123 (2014; Zbl 1306.39007)] are wrong.