On improper integrals and differential equations in ordered Banach spaces

In this paper we study the existence of improper integrals of vector-valued mappings. The so obtained results combined with fixed point results in partially ordered functions spaces are then applied to derive existence and comparison results for least and greatest solutions of initial- and boundary-value problems in ordered Banach spaces. The considered problems can be singular, functional, nonlocal, implicit and discontinuous. Concrete examples are also solved.