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 ẍ+x+aẋ−b(v0+δv(ωt))2(1−x)2=0,and of the Comb-drive model ẍ+x+aẋ−4b(v0+δv(ωt))2x(1−x2)2=0,where x∈R, a, b, v0, δ are positive parameters and v(ωt) is a 2π∕ω-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.