Second order singular boundary value problems with integral boundary conditions

We study the second order singular boundary value problem u″+λf(t,u)=0,t∈(0,1),u(0)=∫01u(s)dξ(s),u(1)=∫01u(s)dη(s). Sufficient conditions are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λλ is also studied. Moreover, application of our theory to a special problem is discussed. To prove our theorem, we utilize some results from the mixed monotone operator theory.