Opuscula Math. 26, no. 3 (2006), 507-514

 
Opuscula Mathematica

Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations

Małgorzata Migda

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.

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  • Małgorzata Migda
  • Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland
  • Received: 2005-08-31.
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Cite this article as:
Małgorzata Migda, Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opuscula Math. 26, no. 3 (2006), 507-514

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