Oscillation theorems for certain delay difference inequalities

Pon Sundar; B.Kishokkumar; K. Revathi

doi:10.26637/MJM0601/0006

Abstract

Our aim in this paper is to give some new results on the oscillatory behavior of all solutions of the delay difference inequalities
$$
x(n)\left\{L_m x(n)+a(n) x(n)+\left(q(n)+p^j(n)\right) x[n-m \tau]\right\} \leq 0 \quad \text { for } m \text { odd }
$$
and
$$
x(n)\left\{L_m x(n)-a(n) x(n)-\left(q(n)+p^j(n)\right) x[n-m \tau]\right\} \geq 0 \text { for } m \text { even }
$$
under the condition $\sum \frac{1}{a_i(s)}=\infty, i=1,2, \cdots, m-1$. Further the result can be extended to more general equations.

Keywords:

Oscillation, Delay terms, Bounded solutions, Linear and Nonlinear, Difference inequalities

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Pon Sundar Department of Mathematics, Om Muruga College of Arts and Science, Mettur, Salem - 636 303, Tamil Nadu, India.
B.Kishokkumar Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal - 637 018, Tamil Nadu, India. https://orcid.org/0000-0003-1000-9773
K. Revathi Department of Mathematics, Sri Sarada Niketan College of Arts and Science, Salem - 636 354, Tamil Nadu, India.

Pages: 41-48
Date Published: 01-01-2018
Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

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