English

Asymptotically polynomial solutions of difference equations of neutral type

Classical Analysis and ODEs 2014-05-09 v1

Abstract

Asymptotic properties of solutions of difference equation of the form Δm(xn+unxn+k)=anf(n,xσ(n))+bn \Delta^m(x_n+u_nx_{n+k})=a_nf(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

Cite

@article{arxiv.1405.1832,
  title  = {Asymptotically polynomial solutions of difference equations of neutral type},
  author = {Janusz Migda},
  journal= {arXiv preprint arXiv:1405.1832},
  year   = {2014}
}