Some oscillation theorems for second order nonlinear neutral type difference equations

E. Thandapani; V. Balasubramanian

doi:10.26637/mjm103/006

Abstract

In this paper some new sufficient conditions for the oscillatory behavior of second order nonlinear neutral type difference equation of the form
$$
\Delta\left(a_n \Delta\left(x_n+p_n x_{n-k}\right)\right)+q_n f\left(x_{\sigma(n+1)}\right)=0
$$
where $\left\{a_n\right\},\left\{p_n\right\}$ and $\left\{q_n\right\}$ are real sequences, $\{\sigma(n)\}$ is a sequence of integers, $k$ is a positive integer and $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous with $u f(u)>0$ for $u \neq 0$ are established. Examples are provided to illustrate the main results.

Keywords:

Nonlinear, neutral type difference equation, oscillation

Mathematics Subject Classification:

39A11

Authors Imprint References Funding Related Articles Downloads

E. Thandapani Ramanujan Institute For Advanced Study in Mathematics, University of Madras, Chennai-600005, Tamil Nadu, India.
V. Balasubramanian Department of Mathematics, Periyar University, Salem-636 011, Tamil Nadu, India.

Pages: 34-43
Date Published: 01-07-2013
Vol. 1 No. 03 (2013): Malaya Journal of Matematik (MJM)

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