Opuscula Math. 26, no. 3 (2006), 507-514
Opuscula Mathematica
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
Abstract. In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form \[\Delta^m(x_n+p_nx_{n-\tau})+f(n,x_{\sigma (n)})=h_n.\] We present conditions under which all nonoscillatory solutions of the above equation have the property \(x_n = cn^{m-1}+o(n^{m-1})\) for some \(c\in R\).
Keywords: neutral difference equation, asymptotic behavior, nonoscillatory solution.
Mathematics Subject Classification: 39A10.
- Małgorzata Migda
- Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland
- Received: 2005-08-31.
