Upper and lower solutions method and a second order three-point singular boundary value problem

The singular boundary value problem {u″+q(t)g(t,u,u′)=0,t∈(0,1),η∈(0,1),γ∈(0,1]u(0)=0,u(1)=γu(η), is studied in this paper.The singularity may appear at t=0t=0 and the function gg may be superlinear at u=∞u=∞ and change sign. The existence of solutions is obtained via an upper and lower solutions method.