Comparison Theorem for Oscillation of Nonlinear Delay Partial Difference Equations

In this paper,we consider certain nonlinear partial difference equations $${(aA_{m+1,n}+bA_{m,n+1}+cA_{m,n})}^k-{(dA_{m,n})}^k+sumlimits_{i=1}^{u} p_{i}(m,n)A^k_{m-sigma_{i},n- au_{i}}=0 $$ where $a,b,c,d in(0,infty )$, $d>c$, $k=q/p$, p, q are positive odd integers, $u$ is a positive integer, $p_{i}(m,n), (i=0,1,2,cdots u)$ are positive real sequences. $sigma_i, au_iin N_{0}={1,2,cdots }, i=1,2,cdots,u$. A new comparison theorem for oscillation of the above equation is obtained.