Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 19-31
doi:10.1155/S1048953303000029

Existence theory for single and multiple solutions to semipositone discrete Dirichlet boundary value problems with singular dependent nonlinearities

Daqing Jiang,1 Lili Zhang,1 Donal O'Regan,2 and Ravi P. Agarwal3

1Northeast Normal University, Department of Mathematics, Changchun 130024, China
2National University of Ireland, Department of Mathematics, Galway, Ireland
3Florida Institute of Technology, Department of Mathematical Sciences, Melbourne 32901, FL, USA

Received 1 September 2002; Revised 1 January 2003

Copyright © 2003 Daqing Jiang 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

In this paper we establish the existence of single and multiple solutions to the semipositone discrete Dirichlet boundary value problem {Δ2y(i−1)+μf(i,y(i))=0,            i∈{1,2,…,T}y(0)=y(T+1)=0, where μ>0 is a constant and our nonlinear term f(i,u) may be singular at u=0.