Oscillation theorems for second-order half-linear neutral difference equations

R. Arula and T.J. Raghupathib,*

Oscillation theorems for second-order half-linear neutral difference equations

Authors :

R. Arul^a and T.J. Raghupathi^b,*

Author Address :

^a,bDepartment of Mathematics, Kandaswami Kandar’s College, Tamil Nadu - 638 182, India.

*Corresponding author.

Abstract :

In this article, some new oscillation criteria are established for the second order neutral difference equation of the form
egin{equation*}
Delta (a(n)Delta (z(n))^alpha) + q(n)x^{alpha}(sigma(n))= 0, ~ ngeq n_0,
end{equation*}
where $z(n)=x(n)+p(n)x( au(n)).$ Our results improve and extend some known results in the literature. Some examples are also provided to show the importance of these results.

Keywords :

Second order, half-linear, neutral, oscillation, difference equations.

DOI :

Article Info :

Received : May 28, 2014; Accepted : July 19, 2014.