Boundedness and Stability for a nonlinear difference equation with multiple delay

Abstract

The equi-boundedness of solutions and the stability of the zero of nonlinear difference equation with bounded multiple delay $$x_{n+1} = \lambda_nx_n+ \sum_{i = 1}^r\alpha^i_nF(x_{n-m_n}), \quad n = 0, 1, \cdots$$ are investigated.