Slowly oscillating solutions in a class of second-order discontinuous delayed systems

This paper investigates the dynamics of oscillations for a class of second-order discontinuous differential equations with time delay. First, by analyzing an implicit function which is determined by a crucial variable of initial values, the existence and uniqueness of a slowly oscillating periodic solution are discussed for equations without the first-degree linear term. And then, under some reasonable assumptions on parameters of the equivalent planar discontinuous systems, analytical conditions for the appearance of bounded slowly oscillating phenomenon are derived with the benefit of geometrical properties of generalized Poincare maps. Finally, two numerical examples are provided to verify the existence of bounded slowly oscillating solutions. This work improves and extends some existing results of other researchers.