Existence of nonoscillatory solutions of higher-order difference equations with positive and negative coefficients
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 23-31 Printed March 1, 2008
Qiaoluan Li, Haiyan Liang, Wenlei Dong, and Zhenguo Zhang Hebei Normal University
Abstract : In this paper, we investigate nonoscillatory solutions of a class of higher order neutral nonlinear difference equations with positive and negative coefficients $$\triangle^{m}(x(n)+p(n)x(\tau(n)))+f_1(n,x(\sigma_{1}(n)))-f_2(n,x(\sigma_{2}(n)))=0,\,\, \,n\geq n_0.$$ Some sufficient conditions for the existence of nonoscillatory solutions are obtained.
Keywords : nonoscillatory, positive and negative coefficients, neutral term
