Oscillation, Nonoscillation and Growth of Solutions of Generalized Nonlinear Difference Equation of Second Order

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Maria Susai Manuel G. B. A. Xavier D. S. Dilip G. Dominic Babu

Abstract

In this paper, the authors discuss oscillation, nonoscillation and growth of solutions of the generalized nonlinear difference equation\begin{equation}\label{6.15.1}\Delta_\ell(p(k)\Delta_\ell u(k))+f(k)F(k,u(k),\Delta_\ell u(k))=g(k,u(k),\Delta_\ell u(k)),\end{equation} \(k\in[a,\infty)\), where the functions \(p\), \(f\), \(F\) and \(g\) are defined in their domain of definition and \(\ell\) is a positive real. Further, \(p(k)>0\) for all \(k\in[a,\infty)\) for some \(a\in[0,\infty)\) and for all \(j=k-a-\Big[\frac{k-a}{\ell}\Big]\ell,R_{a+j,k}\to\infty\), where \[R_{t+j,k}=\sum\limits_{r=0}^{\frac{k-\ell-t-j}{\ell}}\frac{1}{p(t+j+r\ell)},\quad t\in [a,\infty)\text{ and } k\in\mathbb{N}_\ell(t+j+\ell).\]

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How to Cite
MANUEL, Maria Susai et al. Oscillation, Nonoscillation and Growth of Solutions of Generalized Nonlinear Difference Equation of Second Order. Journal of Modern Methods in Numerical Mathematics, [S.l.], v. 3, n. 2, p. 22-34, mar. 2012. ISSN 2090-4770. Available at: <http://www.m-sciences.com/index.php?journal=jmmnm&page=article&op=view&path%5B%5D=302>. Date accessed: 20 sep. 2017. doi: https://doi.org/10.20454/jmmnm.2012.302.
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