Singular nonlocal boundary value problems

This paper presents conditions for the existence of solutions to the differential equation (g(x′))′=f(t,x,x′) satisfying the nonlocal boundary conditions min{x(t):0⩽t⩽T}=0 and Φ(x′)=0. Here positive f satisfies local Carathéodory conditions, f may be singular at the value 0 of both its phase variables and Φ is a functional.