Ulam Stability of Second-Order Periodic Linear Differential Equations with Periodic Damping

We addressed the Ulam stability of second-order periodic linear differential equations with periodic damping. The necessary and sufficient conditions for the Ulam stability of second-order periodic linear differential equations were obtained by providing an Ulam stability theorem and an Ulam instability theorem. In particular, when the elastic coefficient remained constant at 0, a very general conclusion was obtained. These results expand on the conclusions in the relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is provided.