Periodic solutions of the Nathanson's and the Comb-drive models

We provide sufficient conditions for the existence and stability properties of periodic solutions of the second-order non-autonomous differential equation of the Nathanson's model (x) over dot + x + a(x) over dot - b(nu(0) + delta nu(omega t))(2)/(1-x)(2) = 0, and of the Comb-drive model (x) over dot + x + a(x) over dot - 4b(nu(0) + delta nu(omega t))(2)x/(1-x(2))(2) = 0, where x is an element of R, a, b, nu(0), delta are positive parameters and nu(omega t) is a 2 pi/omega-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.