Oscillation theorems for certain delay difference inequalities

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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 :

10.26637/MJM0601/0006

Article Info :

Received : October 12, 2017; Accepted : December 27, 2017.

 

 

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