Theorems on oscillatory and asymptotic behavior of second order nonlinear neutral difference equations

A. Murugesan 1 * and K. Venkataramanan 2

doi:10.26637/MJM0504/0002

Theorems on oscillatory and asymptotic behavior of second order nonlinear neutral difference equations

Authors :

A. Murugesan ^{1 *}and K. Venkataramanan ²

Author Address :

¹ Department of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India.
² Department of Mathematics, Vysya College, Salem-636103, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we discuss a class of second order neutral delay difference equation of the form
egin{equation*}Deltaleft[r(n)left|Delta z(n) ight|^{alpha-1}Delta z(n) ight]+q(n) f(x(n-sigma))=0;quad ngeq n_0quad ag{*}
end{equation*}
where $z(n)=x(n)-p(n)x(n- au)$. We determine sufficient conditions under which every solution of $(*)$ is either oscillatory or tends to zero. Our results improve a number of related results reported in the literature.

Keywords :

Oscillation, nonoscillation, asymptotic behavior, neutral, second order, difference equation.

DOI :

10.26637/MJM0504/0002

Article Info :

Received : June 06, 2017; Accepted : August 07, 2017.