Journal of Applied Mathematics and Stochastic Analysis
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.
Lü, H., O'Regan, D., & Agarwal, R. P. (2006). A positive solution for singular discrete boundary value problems with sign-changing nonlinearities. Journal of Applied Mathematics and Stochastic Analysis, 2006 doi:10.1155/JAMSA.2006.46287