Semicycles of solutions of nonlinear difference equations with several delays

In this paper, we study the semicycles of oscillatory solutions of nonlinear difference equation with several delays where {Pi(n)} is a real sequence with Pi(n) ≥ 0 for all large n; l, mi, kij are positive integers, αij (i = 1, 2,…, l, j = 1, 2,…, mi) are nonnegative real numbers with ∑mij=1 αij = 1, (i = 1, 2,…, l). Upper bound of numbers of terms of semicycles are determined.