Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 46287, 14 pages
doi:10.1155/JAMSA/2006/46287

A positive solution for singular discrete boundary value problems with sign-changing nonlinearities

Haishen Lü,1 Donal O'regan,2 and Ravi P. Agarwal3

1Department of Applied Mathematics, College of Sciences, Hohai University, Nanjing 210098, China
2Department of Mathematics, Faculty of Science, National University of Ireland, Galway, University Road, Galway, Ireland
3Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne 32901-6975, FL, USA

Received 17 February 2005; Revised 1 March 2005; Accepted 2 March 2005

Copyright © 2006 Haishen Lü 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

This paper presents new existence results for the singular discrete boundary value problem −Δ2u(k−1)=g(k,u(k))+λh(k,u(k)), k∈[1,T], u(0)=0=u(T+1). In particular, our nonlinearity may be singular in its dependent variable and is allowed to change sign.