Zhang, B. G.; Zhou, Y. Nonexistence of monotone solutions of neutral partial difference equations. (English) Zbl 1092.39014 Dyn. Syst. Appl. 14, No. 2, 225-244 (2005). The authors consider the neutral partial difference equation \[ T(\Delta_m,\Delta_n)(y(m,n)-p(m,n)y(m-r,n-h))+q(m,n)y(m-k,n-l)=0, \] where \(T(\Delta_m,\Delta_n)=a\Delta_m\Delta_n +b\Delta_m+c\Delta_n+dI\), \(\Delta_{m}y(m,n)=y(m+1,n)-y(m,n)\), \(\Delta_{n}y(m,n)=y(m,n+1)-y(m,n)\), \(Iy(m,n)=y(m,n)\), \(a\), \(b\), \(c\) and \(d\) are nonnegative constants, \(0\leq p(m,n)\leq 1\), \(q(m,n)\geq 0\), the delays \(r\), \(h\), \(k\) and \(l\) are positive integers. The main results of the paper are four theorems in which the authors give sufficient conditions under which the equation has no eventually positive (negative) and nondecreasing (nonincreasing) solution. Reviewer: Gennadij Demidenko (Novosibirsk) Cited in 3 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations Keywords:neutral partial difference equation; nonexistence theorem; positive nondecreasing solution; negative nonincreasing solution PDFBibTeX XMLCite \textit{B. G. Zhang} and \textit{Y. Zhou}, Dyn. Syst. Appl. 14, No. 2, 225--244 (2005; Zbl 1092.39014)