Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 271-283
doi:10.1155/S1085337504306068

Positive solutions for singular discrete boundary value problems

Mariella Cecchi,1 Zuzana Došlá,2 and Mauro Marini1

1Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, Florence 50139, Italy
2Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, Brno 662 95, Czech Republic

Received 10 December 2002

Copyright © 2004 Mariella Cecchi et al. 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.

Abstract

We study the existence of zero-convergent solutions for the second-order nonlinear difference equation Δ(anΦp(Δxn))=g(n,xn+1), where Φp(u)=|u|p−2u, p>1,{an} is a positive real sequence for n≥1, and g is a positive continuous function on ℕ×(0,u0), 0<u0≤∞. The effects of singular nonlinearities and of the forcing term are treated as well.