Necessary and sufficient conditions for oscillation of second order neutral difference equations

Authors

  • E. Thandapani
  • K. Mahalingam

DOI:

https://doi.org/10.5556/j.tkjm.34.2003.260

Abstract

Consider the second order difference equation of the form

$\Delta^2(y\n-py_{n-1-k})+q_nf(y_{n-\ell})=0,\quad n=1,2,3,\ldots  \hskip 1.9cm\hbox{(E)}$

where $ \{q_n\}$ is a nonnegative real sequence, $ f:{\Bbb R}\rightarrow {\Bbb R}$ is continuous such that $ uf(u)>0$ for $ u\not= 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.

Author Biographies

E. Thandapani

Linearized oscillations for even order netural difference equations, Math. Sci. Res. Hot Line 2(1998), 11-17.

K. Mahalingam

Department of Mathematics, Peryiar University, Salem-636011, Tamilnadu, India.

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Published

2003-06-30

How to Cite

Thandapani, E., & Mahalingam, K. (2003). Necessary and sufficient conditions for oscillation of second order neutral difference equations. Tamkang Journal of Mathematics, 34(2), 137-146. https://doi.org/10.5556/j.tkjm.34.2003.260

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Papers