Infinite Horizon Boundary Value Problems and Applications

Abstract

A class of infinite horizon two-point boundary value problems is investigated. Under some monotonicity assumptions, the existence and uniqueness of solutions is proved by means of a homotopy approach and the global exponential asymptotical stability for this class of equations is obtained by choosing an appropriate Lyapunov function. We give a comparison theorem and an application to singularly perturbed problems. © 1999 Academic Press.