On the oscillation of a nonlinear two-dimensional difference systems

Authors

  • E. Thandapani
  • B. Ponnammal

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.375

Abstract

The authors consider the two-dimensional difference system

$$ \Delta x_n = b_n g (y_n) $$

$$ \Delta y_n = -f(n, x_{n+1}) $$

where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

Author Biography

E. Thandapani

Department of Mathematics, Periyar University, Salem - 636 011, Tamilnadu, India.

Published

2001-09-30

How to Cite

Thandapani, E., & Ponnammal, B. (2001). On the oscillation of a nonlinear two-dimensional difference systems. Tamkang Journal of Mathematics, 32(3), 201–209. https://doi.org/10.5556/j.tkjm.32.2001.375

Issue

Section

Papers