OSCILLATION AND NON OSCILLATION
FOR THE SOLUTIONS OF CERTAIN TYPE OF
GENERALIZED NEUTRAL α-DIFFERENCE EQUATION
M. Maria Susai Manuel1, K. Srinivasan2
V. Chandrasekar3, G. Dominic Babu4
1Department of Science and Humanities
R.M.D. Engineering College
Kavaraipettai, 601 206, Tamil Nadu, S. INDIA
2Department of Mathematics
S.K.P. Institute of Technology
Tiruvannamalai, 606 611, S. INDIA
3Department of Science and Humanities
S.K.P. Engineering College
Tiruvannamalai, Tamil Nadu, S. INDIA
4Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Vellore District, Tamil Nadu, S. INDIA
Abstract. In this paper, the authors discuss the oscillation and non oscillation for generalized neutral α-difference equation
\begin{displaymath} \Delta_{\alpha(\ell)}(u(k)+pu(k-\tau\ell))+q(k)u(k-\sigma\ell)=0, \quad k \in [0,\infty), \end{displaymath} (1)

where p is a constant, q(k) is defined on [0,∞), τ is a positive integer and σ is a non-negative integer.
AMS Subject classification: 39A10, 39A11, 39A13, 39A20
Keywords and phrases: generalized $\alpha$-difference equation, oscillation and nonoscillation


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DOI: 10.12732/ijam.v27i2.3

Volume: 27
Issue: 2
Year: 2014