@article{Thandapani_Ponnammal_2001, title={On the oscillation of a nonlinear two-dimensional difference systems}, volume={32}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/375}, DOI={10.5556/j.tkjm.32.2001.375}, abstractNote={<p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: black; font-family: Verdana; mso-font-kerning: 0pt; mso-bidi-font-family: 新細明體;" lang="EN-US">The authors consider the two-dimensional difference system</span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: black; font-family: Verdana; mso-font-kerning: 0pt; mso-bidi-font-family: 新細明體;" lang="EN-US">$$ \Delta x_n = b_n g (y_n) $$ </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: black; font-family: Verdana; mso-font-kerning: 0pt; mso-bidi-font-family: 新細明體;" lang="EN-US">$$ \Delta y_n = -f(n, x_{n+1}) $$</span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt; mso-pagination: widow-orphan;"><span style="font-size: 7.5pt; color: black; font-family: Verdana; mso-font-kerning: 0pt; mso-bidi-font-family: 新細明體;" lang="EN-US">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 e 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.</span></p>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Thandapani, E. and Ponnammal, B.}, year={2001}, month={Sep.}, pages={201–209} }