Asymptotic behavior of solutions of nonlinear higher-order neutral type difference equations

To study the asymptotic behavior of solutions of m th-order neutral type difference equations of the form Delta(m)(y(n) + py(n-k)) = f(n,y(n-1),Delta y(n-l), Delta(2)y(n-l),..., Delta(m-1)y(n-l)) n, m is an element of N using some difference inequalities. We establish conditions under which all the nonoscillatory solutions are asymptotic to polynomial a(1)n(m-1) + a(2)n(m-2) +...+ a(m-1)n+a(m) as n -> infinity with a(i) is an element of R, i = 1,2,...m .