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

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.