Asymptotically polynomial solutions of difference equations of neutral type
Abstract
Asymptotic properties of solutions of difference equation of the form \[ m(xn+unxn+k)=anf(n,xσ(n))+bn \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or all nonoscillatory solutions are asymptotically polynomial. We use a new technique which allows us to control the degree of approximation.
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