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 x(n+1) - x(n) + Sigma (l)(i=1) P-i(n) Pi (mi)(j=1) \x(n-kij)\(alpha ij) sign x(n-kij) = 0, where {P-i(n)} is a real sequence with P-i(n) greater than or equal to 0 for all large n; l, m(i), k(ij) are positive integers, alpha (ij) (i = 1, 2,..., l,j = 1,2,..., m(i)) are nonnegative real numbers with Sigma (mi)(j=1) alpha (ij) = 1, (i = 1,2,...,l). Upper bound of numbers of terms of semicycles are determined. (C) 2001 Elsevier Science Ltd. All rights reserved.
semicycles difference equations oscillation