Asymptotic behavior of solutions of certain higher order nonlinear difference equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:205

Article

Yao, Jianli ; Meng, Fanwei

关键词: difference equation;    asymptotic behavior of solutions;    discrete inequality;   

DOI  :  10.1016/j.cam.2006.05.039

来源: Elsevier

【 摘 要 】

In this paper, we consider the higher order difference equation y(k + n) + p(1) (k)y(k + n - 1) + p(2)(k)y(k + n - 2) + center dot center dot center dot + p(n)(k)y(k) =f[k, y(k), y(k + 1), . . . , y(k + n - 1), Sigma k-1s=k0 g(k, s, y(s), y(s + n -1))], k epsilon N(k(0))={k(0), k(0) + 1, k(0) + 2, . . .), k(0) epsilon {1, 2, . . . .}. With the aid of a discrete inequality, we obtain some sufficient conditions which guarantee that for every solution y(k) of (1) satisfies the equation as k -> infinity, y(k) = Sigma ni=1 (delta(i) + o(1))z(i) (k), where delta(i), i = 1, 2, . . ., n are constants, {z(i){k)}(n)(i=1) are any independent solutions of the equation z(k + n) + p(1) (k)z(k + n - 1) + p(2)(k)z(k + n - 2) + center dot center dot center dot + p(n)(k)z(k) = 0, k epsilon N (k(0)). (C) 2006 Elsevier B.V. All rights reserved.

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