Asymptotic properties of fourth-order nonlinear difference equations

We consider a class of fourth-order nonlinear difference equations of the form Delta(a(n)Delta(b(n)Delta(c(n)Deltay(n)))) + f(n, y(n)) = 0, where a, b,c : N --> R+ and (a(n)) is bounded away from zero, a(n) greater than or equal to c(n), the series Sigma(i=1)(infinity)(1/a(i)) is convergent and Sigma(j=1)(infinity) (1/c(j)) Sigma(i=j)(infinity) (1/b(i)) is divergent. The classification of nonoscillatory solutions is given. Sufficient conditions for the above equation are obtained to admit the existence of nonoscillatory solutions with special asymptotic properties. (C) 2004 Elsevier Ltd. All rights reserved.