Electronic Journal of Differential Equations (Jan 2007)

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

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

Journal volume & issue
Vol. 2007, no. 09
pp. 1 – 7

Abstract

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In this paper, we consider the higher order neutral nonlinear difference equation$$displaylines{ Delta^{m}(x(n)+p(n)x(au(n)))+f_1(n,x(sigma_{1}(n))) -f_2(n,x(sigma_{2}(n)))=0, cr Delta^{m}(x(n)+p(n)x(au(n)))+f_1(n,x(sigma_{1}(n))) -f_2(n,x(sigma_{2}(n)))=g(n), cr Delta^{m}(x(n)+p(n)x(au(n)))+sum_{i=1}^{l}b_i(n)x(sigma_i(n))=0.}$$ We obtain sufficient conditions for the existence of non-oscillatory solutions.

Keywords