A nonlocal heat flow problem (Q1826781)

The considered steady-state heat-flow problem leads to the nonlocal boundary value problem \[ u''=F(x,u),\quad 0<x<1, \] \[ u(0)=u_0,\quad \int^1_\xi g(x,u(x))\,dx=b\text{ with }\xi\in(0,1]. \] Under suitable assumptions on \(F\) and \(g\), the author proves existence, uniqueness and monotonicity of the solution.