On a delay reaction-diffusion difference equation of neutral type (Q1565992)

A new proof for a nonoscillatory solution of a delay difference equation of neutral type is established. Further it is proved that every nonoscillatory solutions of \[ \Delta_r (u_{n,m}+ pu_{n-k}, m)+ q_{n,m} u_{n-l,m}= a^2\Delta^2_2 u_{n+1,m-1} \] goes uniformly in \(m\), \(n\to\infty\) and tends to (1) zero, if \(p\geq -1\); (2) \(\infty\), if \(p<-1\); and (3) oscillates if \(p= -1\).