International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2769-2774

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

Anna Kisiolek1 and Ireneusz Kubiaczyk2

1Institute of Mathematics, Poznan University of Technology, 5 Maria Sklodowska-Curie Square, Poznan 60-965, Poland
2Collegium Mathematicum, Adam Mickiewicz University, Umultowska 87, Poznan 61-614, Poland

Received 1 June 2005

Copyright © 2005 Anna Kisiolek and Ireneusz Kubiaczyk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the second-order nonlinear difference equations of the form Δ(rn1Δxn1)+pnf(xnk)=hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour xnaj=0n1(1/rj)+b=o(1), a,b. 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.