Existence of nonoscillatory solutions of higher-order difference equations with positive and negative coefficients

Qiaoluan Li; Haiyan Liang; Wenlei Dong; Zhenguo Zhang

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2008; 45(1): 23-31

Printed March 1, 2008

Existence of nonoscillatory solutions of higher-order difference equations with positive and negative coefficients

Qiaoluan Li, Haiyan Liang, Wenlei Dong, and Zhenguo Zhang

Hebei Normal University

Abstract

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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

MSC numbers: 39A10,39A05