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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 34232, 7 pages
http://dx.doi.org/10.1155/IJMMS/2006/34232

Oscillation of solutions of impulsive neutral difference equations with continuous variable

1Department of Mathematics, Huaihua College, Huaihua, Hunan 418008, China
2Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China

Received 21 June 2005; Revised 1 April 2006; Accepted 25 April 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain sufficient conditions for oscillation of all solutions of the neutral impulsive difference equation with continuous variable Δτ(y(t)+p(t)y(tmτ))+Q(t)y(tlτ)=0, tt0τ, ttk, y(tk+τ)y(tk)=bky(tk), k(1), where Δτ denotes the forward difference operator, that is, Δτz(t)=z(t+τ)z(t), p(t)C([t0τ,),), Q(t)C([t0τ,),(0,)), m, l are positive integers, τ>0 and bk are constants, 0t0<t1<t2<<tk< with limktk=.