Positive solutions of nonlinear singular boundary value problems in abstract spaces

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