Studies in Mathematical Sciences
Oscillation of Nonlinear Delay Partial Difference Equations
Abstract
In this paper, we consider certain nonlinear partial difference equations
$$aA_{m+1,n}+bA_{m, n+1}-cA_{m,n}+\sum\limits_{i=1}^{u} p_{i}(m,n)A_{m-\sigma_{i},n-\tau_{i}}=0 $$
where $a,b,c\in(0,\infty )$, $u$ is a positive integer, $p_{i}(m,n),~(i=0,1,2,\cdots u)$ are positive real sequences. $\sigma_i,\tau_i\in N_{0}=\{1,2,\cdots \},~i=1,2,\cdots,u$. A new comparison theorem for oscillation of the above equation is obtained.
$$aA_{m+1,n}+bA_{m, n+1}-cA_{m,n}+\sum\limits_{i=1}^{u} p_{i}(m,n)A_{m-\sigma_{i},n-\tau_{i}}=0 $$
where $a,b,c\in(0,\infty )$, $u$ is a positive integer, $p_{i}(m,n),~(i=0,1,2,\cdots u)$ are positive real sequences. $\sigma_i,\tau_i\in N_{0}=\{1,2,\cdots \},~i=1,2,\cdots,u$. A new comparison theorem for oscillation of the above equation is obtained.
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