Oscillatory Behaviors of Solutions of Riccati'S \(\alpha\)-Difference Equation

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Maria Susai Manuel Chandrasekar V Britto Antony Xavier G

Abstract

In this paper, by introducing $\alpha$-difference equation with the definition of generalized $\alpha$-difference operator, we discuss the oscillatory and nonoscillatory behaviours of the solutions of the Riccati's generalized $\alpha$-difference equation

\[{\label{trans.01}}\Delta_{\alpha(\ell)}\big(p(k)\Delta_{\alpha(\ell)} u(k)\big)+\alpha r(k) u(k+\ell) = 0, \ k\in[0, \infty), \ \alpha > 0\]

where the real valued functions $p > 0$ and $r$ are defined on $[0,\infty)$ and $\Delta_{\alpha(\ell)} u(k) = u(k+\ell) - \alpha u(k)$.

Article Details

How to Cite
MANUEL, Maria Susai; V, Chandrasekar; XAVIER G, Britto Antony. Oscillatory Behaviors of Solutions of Riccati'S \(\alpha\)-Difference Equation. Journal of Modern Methods in Numerical Mathematics, [S.l.], v. 4, n. 1, p. 11:22, oct. 2012. ISSN 2090-4770. Available at: <http://www.m-sciences.com/index.php?journal=jmmnm&page=article&op=view&path%5B%5D=442>. Date accessed: 21 oct. 2017. doi: https://doi.org/10.20454/jmmnm.2013.442.
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