IJPAM: Volume 105, No. 2 (2015)

ASYMPTOTIC AND OSCILLATORY BEHAVIOUR OF
SOLUTIONS OF THIRD ORDER GENERALIZED
MIXED DIFFERENCE EQUATION

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, S. INDIA


Abstract. In this paper, the authors discuss the asymptotic and oscillatory behaviour of solutions of the third order generalized mixed difference equation of the form

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

where $p(k)\geq0$ and $\alpha,\ell$ are positive reals.

Received: August 28, 2015

AMS Subject Classification: 39A12

Key Words and Phrases: generalized mixed difference equation, oscillation and asymptotic

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DOI: 10.12732/ijpam.v105i2.7 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: 2015
Volume: 105
Issue: 2
Pages: 201 - 211


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