Oscillation criteria for certain even order quasilinear difference equations (Q1034987)

By assuming that \(\sigma(n) \leq n\) is a real increasing sequence and \(f(n,u) \, \text{sgn} \,u \geq q_n\, |u|^{\alpha-1}u\), with \(q_n\) a positive sequence, the author gives a new oscillation criterion for the high order quasilinear difference equation \[ \Delta(|\Delta^{k-1}x_n|^{\alpha-1} \Delta^{k-1}x_n)+f(n,x_{\sigma(n)})=0. \] Here \(n \in \{0,1,2,\dots\}\), \(\Delta x_n=x_{n+1}-x_n\) and \(\Delta^dx_n=\Delta(\Delta^{d-1}x_n)\). \(\alpha \geq 1\) is a constant and \(k\) is an even integer.