Periodic solutions of some classes of continuous third-order differential equations

We study the periodic solutions of the third-order differential equations of the form x⃛±xn=μf(t), or x⃛±|x|n=μf(t), where n=2,3,…,f(t) is a continuous T− periodic function such that ∫0Tf(t)dt≠0, and µ is a positive small parameter. Note that the differential equations x⃛±xn=μf(t) are only continuous in t and smooth in x, and that the differential equations x⃛±|x|n=μf(t) are only continuous in t and locally-Lipschitz in x. We also study the stability of the periodic solutions.