IJPAM: Volume 96, No. 1 (2014)

GLOBAL PROPERTIES OF SOLUTIONS OF FOURTH
ORDER GENERALIZED $\alpha-$DIFFERENCE EQUATIONS

M. Maria Susai Manuel$^1$, K. Srinivasan$^2$, D.S. Dilip$^3$, G. Dominic Babu$^4$
$^1$Department of Science and Humanities
R.M.D. Engineering College
Kavaraipettai, 601 206, Tamil Nadu, S. INDIA
$^2$Department of Science and Humanities
S.K.P. Institute of Technology
Tiruvannamalai, Tamil Nadu, S. INDIA
$^3$Department of Mathematics
St. John's College
Anchal, Kollam District, Kerala, INDIA
$^4$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Vellore District
Tamil Nadu, S. INDIA


Abstract. In this paper, the authors discuss various properties of solutions for the generalized $\alpha-$difference equation

\begin{displaymath} \Delta_{\alpha(\ell)}^4u(k-2\ell)=\alpha^2p(k)u(k),\quad k\in[2\ell,\infty), \end{displaymath} (1)

where the functions $p$ is positive on $[2\ell,\infty)$, $\alpha>1$ and $\ell$ is a positive real.

Received: July 9, 2014

AMS Subject Classification: 39A, 12

Key Words and Phrases: generalized $\alpha-$difference equation, generalized $\alpha-$difference operator, oscillation and nonoscillation

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DOI: 10.12732/ijpam.v96i1.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 96
Issue: 1
Pages: 117 - 134


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