Oscillation theorems for certain delay difference inequalities
Authors :
Pon Sundar1*, B.Kishokkumar2 and K. Revathi3
Author Address :
1Department of Mathematics, Om Muruga College of Arts and Science, Mettur, Salem - 636 303, Tamil Nadu, India.
2Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal - 637 018, Tamil Nadu, India.
3Department of Mathematics, Sri Sarada Niketan College of Arts and Science, Salem - 636 354, Tamil Nadu, India.
*Corresponding author.
Abstract :
Our aim in this paper is to give some new results on the oscillatory behavior of all solutions of the delay difference inequalities
egin{align*}
x(n)left{L_mx(n)+a(n)x(n)+(q(n)+p^j(n))x[n-m au] ight}le 0 quad mbox{for} m mbox{odd}
end{align*}
and
egin{align*}
x(n)left{L_mx(n)-a(n)x(n)-(q(n)+p^j(n))x[n-m au] ight}ge 0 quad mbox{for} m mbox{even}
end{align*}
under the condition $sumlimits^{infty}dfrac{1}{a_i(s)}=infty$, $i=1,2,cdots, m-1$. Further the result can be extended to more general equations.
Keywords :
Oscillation, Delay terms, Bounded solutions, Linear and Nonlinear, Difference inequalities.
DOI :
Article Info :
Received : October 12, 2017; Accepted : December 27, 2017.
