Oscillation theorems for second order neutral difference equations with “Maxima”

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Authors :

S.Rajan 1 * and K.Malathi 2

Author Address :

1 Department of Mathematics, Erode Arts and Science College, Erode - 638 009, Tamil Nadu, India.
2 Department of Mathematics, Kongu Arts and Science College, Erode - 638 107, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper we establish some sufficient conditions for the
oscillation of all solutions of the equation
$$ Delta(r_n Delta(x_n +p_n x_{n-k} ))+q_n max_{[n-ell, n]}x_{s}^alpha = 0, nin N_0$$
which improve and extend the known results. Examples are provided to illustrate the main results.

Keywords :

Second order, oscillation, neutral difference equation with ``maxima’’.

DOI :

10.26637/MJM0602/0019

Article Info :

Received : November 12, 2017; Accepted : February 18, 2018.

 

 

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