On the count and the classification of periodic solutions to forced pendulum-type equations
The pendulum-type problem of the form \[ \ddot {u}+V'(u(t)) = h(t) +\lambda , \] \(u\) is \(T\)-periodic, \(\lambda \in \mathbb{R}\), is studied under some assumptions on \(T\) and the forcing \(h\). The main assumption is \(\max V'' <(\frac {2\pi }{T})^2\) and that \(V'\) is a Morse function with distinct critical values. A one-to-one correspondence of solutions to the present problem to an auxiliary one for the so-called reduction function is shown. For the auxiliary equation, the number of its pre-images describes the number of the solutions to the original problem and this is the main tool for the considerations in the paper.
scientific article; zbMATH DE number 1453646