Comparison theorems for the oscillation of higher order difference equations with deviating arguments (Q1370679)

Consider the difference equation \[ \Delta^\alpha y(n)+\delta p(n)f(y(g(n)))=0 \tag \(*\) \] where \(p(n)\) is positive, \(\alpha\) is odd or even and \(\delta\) is \(+1\) or \(-1\). In each case, the authors offer comparison theorems for the oscillation of the difference equation \((*)\) with \[ \begin{aligned} &\Delta^\alpha y(n)+\delta q(n)f(y(h)n)))=0\\ \text{or} &\Delta^\alpha y(n)+ \delta p(n) f(y(n))=0. \end{aligned} \] The results obtained here are discrete analogues of some of the results of \textit{D. L. Lovelady} [Pac. J. Math. 57, 475-480 (1975; Zbl 0305.34054)], \textit{J. J. A. M. Brands} [J. Math. Anal. Appl. 63, 54-64 (1978; Zbl 0384.34049)] and \textit{R. Oláh} [Arch. Math., Brno 16, 213-216 (1980; Zbl 0447.34065)].