in this paper we consider the second order nonlinear neutral delay partial difference equation $delta_ndelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$under suitable conditions, by making use of the banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

and Applied Analysis 3 Let l∞ β denote the Banach space of all bounded sequences in Zβ with norm ‖x‖ sup n∈Zβ |xn| for x {xn}n∈Zβ ∈ l∞ β , B d,D { x {xn}n∈Zβ ∈ l∞ β : ‖x − d‖ ≤ D } for d {d}n∈Zβ ∈ l∞ β , D > 0 2.2 represent the closed ball centered at d and with radius D in l∞ β . By a solution of 1.1 , we mean a sequence {xn}n∈Zβ with a positive integer T ≥ n0 τ |β| such that 1.1 is satisfied ...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples. Key...