IJPAM: Volume 106, No. 2 (2016)

OSCILLATORY AND NONOSCILLATORY BEHAVIOUR OF
SOLUTIONS OF GENERALIZED MIXED
DIFFERENCE EQUATIONS

M. Maria Susai Manuel$^1$, G. Dominic Babu$^2$, D.S. Dilip$^3$, G. Britto Antony Xavier$^4$
$^1$Department of Mathematics, R.M.D. Engineering College,
Kavaraipettai - 601 206, Tamil Nadu, S. INDIA
$^2$Department of Mathematics
Annai Velankanni College
Tholaiyavattam, Kanyakumari District, INDIA
$^3$Department of Mathematics
St. John's College, Anchal, Kollam Dt., INDIA
$^4$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Vellore District,Tamil Nadu, INDIA


Abstract. In this paper, the authors discuss the oscillatory and nonoscillatory behaviour of solutions of some generalized mixed difference equations of the form

\begin{displaymath} \Delta_{\ell}^2\Big(\Delta_{\alpha(\ell)} u(k)\Big)+\delta p(k)u(k)=0, k\in[a,\infty), \end{displaymath} (1)


\begin{displaymath} \Delta_{\ell}^3\Big(\Delta_{\alpha(\ell)} u(k)\Big)+\delta p(k)u(k)=0, k\in[a,\infty), \end{displaymath} (2)

where $\delta=\pm1$ and the function $p$ is real with $p(k)\geq c$ and $\alpha,\ell$ are positive real.

Received: November 16, 2015

AMS Subject Classification: 39A12

Key Words and Phrases: generalized difference operator, mixed difference equation, oscillation and nonoscillation

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DOI: 10.12732/ijpam.v106i2.26 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: 2016
Volume: 106
Issue: 2
Pages: 639 - 647


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