Positive solutions of nonlinear singular boundary value problem in abstract space

By constructing a particular closed convex set and applying the Mönch fixed-point theorem, we study the existence of apositive solutions of singular boundary value problem x″(t)+f(t,x(t))=θ, tε(0,1), x(0)+x(1)=θ, in Banach space, singularities occuring at t = 0, 1, and X = φ. Our method is completely distinct from what the former literatures used even if we discuss the above problem in scalar space.