IJPAM: Volume 59, No. 1 (2010)

OSCILLATION FOR A NONLINEAR SECOND-ORDER
DIFFERENCE EQUATION IN ARCHIMEDEAN SPACE

Lili Zhao$^1$, Yuchun Hua$^2$
$^{1,2}$Department of Mathematics
Yunnan University
Kunming, Yunnan, 650091, P.R. CHINA
$^1$e-mail: llzhao@ynu.edu.cn


Abstract.In Archimedean space $(X,\prec)$ we study the oscillation of solutions of the second-order difference equation of the form
\begin{multline*} \Delta\big[p(k)\Psi(y(k))\Delta y(k)\big]+q(k)h(y(k))g(\Delta ... ...(k)))\Delta y(k)\\ +f(k,y(k),y(k-r_1(k)),\ldots,y(k-r_n(k)))=0, \end{multline*}
where $\mathbb{N}=\{0,1,2,\ldots\},\,\mathbb{N}(k_0)=\{k_0,k_0+1,\ldots\},\,k_0\in\mat... ...}\rightarrow X,\,r,r_i:\mathbb{N}(k_0)\rightarrow \mathbb{N},\, i=1,2,\ldots,n$. Our results are new and complement of previously known results. Also, three examples are given to show the effectiveness of the proposed method and results.

Received: January 11, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: order relation, second-order difference equation, oscillation, Archimedean space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 1