@article{Thandapani_Mahalingam_2003, title={Necessary and sufficient conditions for oscillation of second order neutral difference equations}, volume={34}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/260}, DOI={10.5556/j.tkjm.34.2003.260}, abstractNote={<p>Consider the second order difference equation of the form</p><p>$\Delta^2(y -py_{n-1-k})+q_nf(y_{n-\ell})=0,\quad n=1,2,3,\ldots  \hskip 1.9cm\hbox{(E)}$</p><p>where $ \{q_n\}$ is a nonnegative real sequence, $ f:{\Bbb R}\rightarrow {\Bbb R}$ is continuous such that $ uf(u)>0$ for $ u ot= 0$, $ 0\le p<1$, $ k$ and $ \ell$ are positive integers. We establish the necessary and/or sufficient conditions for the oscillation of all solutions of (E) when $ \int$ is linear, superlinear or sublinear and the results reduce to the well known theorems of Hooker and Patula in the special case when $ f(u)=u^\gamma$, where $ \gamma$ is a odd positive integers.</p>}, number={2}, journal={Tamkang Journal of Mathematics}, author={Thandapani, E. and Mahalingam, K.}, year={2003}, month={Jun.}, pages={137–146} }