Asymptotically polynomial solutions to difference equations of neutral type. (English) Zbl 1410.39002
Summary: Asymptotic properties of solutions to difference equation of the form \[ \Delta^m(x_n + u_n x_{n + k}) = a_n f(n, x_{\sigma(n)}) + b_n \] 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.
Keywords:
difference equation; neutral equation; asymptotic behavior; asymptotically polynomial solution; nonoscillatory solutionReferences:
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