Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 09, pp. 1-7.

Title: Existence of non-oscillatory solutions to higher-order
       mixed difference equations

Authors: Qiaoluan Li   (Zhejiang Ocean Univ., China)
         Haiyan Liang  (Zhejiang Ocean Univ., China)
	 Wenlei Dong   (Zhejiang Ocean Univ., China)
	 Zhenguo Zhang (Zhejiang Ocean Univ., China)

Abstract:
 In this paper, we consider the higher order neutral nonlinear
 difference equation
$$\displaylines{
 \Delta^{m}(x(n)+p(n)x(\tau(n)))+f_1(n,x(\sigma_{1}(n)))
 -f_2(n,x(\sigma_{2}(n)))=0, \cr
 \Delta^{m}(x(n)+p(n)x(\tau(n)))+f_1(n,x(\sigma_{1}(n)))
 -f_2(n,x(\sigma_{2}(n)))=g(n), \cr
 \Delta^{m}(x(n)+p(n)x(\tau(n)))+\sum_{i=1}^{l}b_i(n)x(\sigma_i(n))=0.
}$$
 We obtain  sufficient conditions for the existence of non-oscillatory
 solutions.
 
Submitted April 30, 2006. Published January 2, 2007.
Math Subject Classifications: 39A05, 39A10.
Key Words: Nonoscillatory; existence; neutral equation.