On Periodic Solutions of a Second-Order Ordinary Differential Equation

We consider a differential equation containing first- and second-order forms with respect to the phase variable and its derivative with constant coefficients and a periodic inhomogeneity. Using the method of constructing a positively invariant rectangular domain, we examine the existence of a asymptotically stable (in the Lyapunov sense) periodic solution. Criteria for the existence of a periodic solution are formulated in terms of properties of isoclines. We consider cases where the zero isocline is a nondegenerate second-order curve.