Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument

Qualitative behaviors of first-order delay differential equations with piecewise constant arguments are the subject of many investigations see, e.g., 1–19 , while those of higherorder equations are not. However, there are reasons for studying higher-order equations with piecewise constant arguments. Indeed, as mentioned in 10 , a potential application of these equations is in the stabilization of hybrid control systems with feedback delay, where a hybrid system is onewith a continuous plant andwith a discrete sampled controller. As an example, suppose that a moving particle with time variable mass r t is subjected to a restoring controller −φ x t which acts at sampled time t . Then Newton’s second law asserts that