In this paper, we establish some necessary conditions on the nonoscillation of the nonlinear difference equation DELTApsi(DELTAx(k-1) + a(k) psi(x(k)) = 0, k = 1, 2,..., (E) where psi:R --> R is defined by psi(s) = [s]p-2 s with p > 1 a fixed real number, and {a(k)}1infinity is a nonnegative sequence with infinitely many positive terms.
