The minimal period problem for the classical forced pendulum equation

Considered in this paper is the existence/nonexistence of periodic solutions with prescribed minimal periods to the classical forced pendulum equation,x¨+Asinx=f(t), where A=g/lA=g/l is a constant with g being the gravity constant and l being the length of the pendulum, and f is a T-periodic function which is regarded as an external force. The new results are obtained by applying the critical point theory and by using an original decomposition technique to better estimate the critical values associated with a variational functional.