C(I)C(I) Positive solutions of nonlinear singular differential equations for nonmonotonic function terms

Suppose f(t,u,v)f(t,u,v) is nonnegative, continuous on (0,1)×R+×R+(0,1)×R+×R+, and nondecreasing on uu and nonincreasing on vv for each fixed tt, there exist real numbers a∈(0,1),b∈(0,+∞)a∈(0,1),b∈(0,+∞) such that, for any 00αγ+αδ+βγ>0, and G(t,s)G(t,s) is Green’s function of the above problem (when f(x,u,u)=0f(x,u,u)=0).