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