Boundary value problems involving upper and lower solutions in reverse order

In this paper, we discuss the existence of extreme solutions of the boundary value problem for a class of first-order functional equations with a nonlinear boundary condition. In the presence of a lower solution α$\alpha$ and an upper solution β$\beta$ with β≤α$\beta \le \alpha$, we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique.