| Abstract: |
| In this article, the necessary and sufficient conditions for the oscillation of a class of nonlinear second order neutral impulsive difference equations of the form:
$$
\begin{cases}
\Delta[a(n)\Delta(x(n)+p(n)x(n -\tau))] +q(n)F(x(n -\sigma))=0,\, n\neq m_j,\,j\in\mathbb{N} \\
\underline{\Delta}[a(m_j-1)\Delta(x(m_j-1)+p(m_j-1)x(m_j-\tau-1))]+r(m_j-1)F(x(m_j-\sigma-1))=0
\end{cases}
$$
have been discussed for different ranges of the neutral coefficient $p(n)$, $|p(n)|< \infty$ with fixed moments of impulsive effect. Here, we assume that the nonlinear function is either strongly sublinear or strongly superliner. Some examples are given to illustrate our main results. |
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