Almost-periodic oscillations of monotone second-order systems

Abstract

We study the bounded and the a.p. (almost-periodic) solutions of forced second order systems with monotone fields and a linear damping term. A special class of such systems is the class of the second order Lagrangian systems with convex Lagrangians. We provide results of existence and uniqueness, we study the dependence of the bounded and a.p. solutions on the bounded and a.p. forcing terms, and finally we treat the case where an additional small nonlinear damping term is present in the equation.