Existence of solutions of differential equations with nonlinear multipoint boundary conditions (Q1767827)

Consider the multipoint boundary value problem \[ x'(t)=f\bigl(t,x(t) \bigr),\;t\in J=[0,T],\;T>0,\quad 0=g\bigl(x(t_0),x(t_1), \dots,x(t_r) \bigr) \] with \(0=t_0<t_1<t_2<\cdots<t_{r-1}<t_r=T\), \(f\in C(J \times \mathbb{R},\mathbb{R})\), and \(g\in C(\mathbb{R}^{r+1}, \mathbb{R})\). The author establishes the existence of extremal solutions or of a unique solution by means of the technique of monotone iteration.