## Oscillation of nonlinear difference equations with several coefficients.(English)Zbl 1163.39004

Summary: We provide some sufficient conditions for the oscillation of every solution of the following linear difference equation:
$x_{n+1}-x_n +\sum^m_{i=1} p_{in} x_{n-k_i}=0,$
where $$k_i\in\{\dots,-3,-2\}$$ and $$p_{in}\leq 0$$ for $$i =1,2,\dots,m$$. Furthermore, we consider the oscillation properties of the following nonlinear difference equations
\begin{aligned} &x_{n+1}-x_n+(1+x_n)\sum^m_{i=1} p_{in}x_{n-k_i}=0,\\ & x_{n+1}-x_n+\sum^m_{i=1} p_{in} f_i(x_n-k_i)=0,\end{aligned} in the cases $$k_i\in\{0,1,\dots\}$$ and $$p_{in}\geq 0$$ for $$i=1,2,\dots,m$$.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations