Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces (Q2368398)

The authors consider the second-order nonlinear difference equation of the form \((r_{n-1}x_{n-1})+p_{n}f(x_{n-k})=h_{n}\). They show that there exists a solution \((x_{n})\), which possesses the asymptotic behaviour \(| x_{n}-a \sum_{j=0}^{n-1}((1/(r_{j})))+b|=o(1)\), \(a,b \in {\mathbb R}\).