Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

Abstract

We consider the second‐order nonlinear difference equations of the form Δ(rn−1Δxn−1) + pnf(xn − k) = hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour , a, b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.