Oscillation for partial difference equations with continuous variables

摘要

In this paper, we develop criteria for oscillation of the partial difference equation with continuous variables of the form Au(x+a,y+b)+Bu(x+a,y)+Cu(x,y+b)−u(x,y)+D(x,y)u(x−τ,y)+E(x,y)u(x,y−σ)+F(x,y)u(x−τ,y−σ)=0,where D,E,F∈C(R+×R+,R+−{0}), A,B and C are nonnegative constants, a,b,τ and σ are positive constants. Several examples which dwell upon the importance of our results are also included.