On the asymptotic behavior of solutions of a nonlinear difference equation with bounded multiple delay (Q863774)

The paper deals with the difference equation \[ x_{n+1} = \lambda_n x_n + \sum_{i=1}^r \alpha_i(n) F(x_{n-m_i}), \;n =0,1,..., \eqno(1) \] where \(r, m_i, 1 \leq i \leq r,\) are fixed positive integers. If \(\lambda_n \equiv 1\) and \(xF(x) < 0, x \neq 0,\) conditions for the oscillation of all solutions of (1) are obtained. If \(\lambda_n \in (0, 1)\) and coefficients \(\alpha_i\) don't depend on \(n\), the author gives conditions for boundedness and convergence to zero of every solution and conditions for the existence of a periodic solution of (1).