Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

This paper studies the existence of solutions to the singular boundary value problem {-u'' = g(t,u) + (h,u),t ∈ (0,1), u(0) = 0 = u(1), where g: (0, 1) × (0, ∞) → R and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.