OSCILLATORY AND ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL-TYPE DIFFERENCE-EQUATIONS

The authors consider the higher-order nonlinear neutral delay differen ce equation Delta(m)[y(n-m+1) + p(n-m+1Yn-m+1-k)] + delta F(n, y(n-1)) = 0 and obtain results on the asymptotic behavior of solutions when { p(n)} is allowed to oscillate about the bifurcation value -1. We also consider the case where the sequence {p(n)} has arbitrarily large zero s. Examples illustrating the results are included, and suggestions for further research are indicated.